Questions on GSSR and in General

1. I dunno what you mean by "deliberate"? Yes, most banners don't have many options, but they are only including all the non-limited SSR servants, and so far there haven't been many of them.

2. The game is pretty much entirely f2p. There is no competitive element, and almost everything in the game (at least as far as the story is concerned) is doable with just 3* servants and below. On top of that, the game offers regular events that give you 4* servants at NP5 for free, and on top of that, you can always borrow strong servants from your friend list. Add to that, I see you have literally the three best supports in the game. There's practically no problem for you.

Assassin is a good banner to roll, and so is lancer, really up to you which to pick. Personally I'd go with assassin just because the servants on it are a bit better imo, though the servants in the lancer banner all have more synergy with Merlin to varying degrees.

Tamamo/Vlad aren't great with one-shot burst, they are pretty famously a sustain-focused team. Using Altera also isn't a great idea, her NP is AOE so it does less damage to a single enemy than other servants. To one-shot pillars, you need a combination of higher NP levels, suitable servants (pretty much going to want buster-focused, offensive servants with single-target NPs for this one), good CEs geared specifically toward increasing the damage of one servant (ox-demon king is particularly good for demon pillars on supports, since it gives a damage bonus to other servants in the party too). Usually one-shotting is done with servants like Heracles/Ozymandias/Quetzalcoatl, all with high bond for a higher damage multiplier during Solomon and support Merlins/Wavers to charge NP and buff damage.

As for the teams you are using, you are free to use any team you want, but the ones you have been using don't have that much synergy. Usually when building teams, there are two ways to do it. You can look at what enemy classes will be in that quest, then include servants that are strong against that class, ie using servants like Iskandar against casters. Berserkers are sought-after early on because they are a blanket class that deals strong damage against everything.

The other way is to form your own teams based on what goes well together for a particular strategy. A very common team is Jeanne D'Arc Alter + Merlin + Merlin, for example. Merlins buff Jalter's buster card effectiveness, and his NP gives stars, heal and NP gain over time. This is perfect for Jalter because she has a critical star absorb skill + critical damage buff, is relatively frail so benefits form the heal, and has her own NP charge over time, so there's your synergy. What results is Jalter almost never having her health drop below 50%, being able to fire off her NP every other turn, and that NP being buffed to be extremely strong and then Jalter dealing massive critical damage on top of that.

Another example more applicable to your case is Vlad + Tamamo + Jeanne/Tamamo. This is also effective as Vlad relies on his first skill and chaining his arts cards to gain NP since his base NP gain rate is bad, and Tamamo can help him with both these things. Tamamo also has an arts buff that will benefit Vlad's damage. Two Tamamos with Vlad is really impressive, but Jeanne is also used for her tankiness and general defensive support since Vlad is relatively frail.

3. Buster/arts crit teams run servants/craft essences that help them gain critical stars so that they can perform criticals a lot. Merlin is perfect for buster-crit because his third skill buffs both buster effectiveness and critical strength, and his NP gives you stars. 2030 is a good CE for these as it grants critical stars every turn, as well as joint recital/another ending/victor of the moon as they buff buster/arts damage and crit strength. An optimal buster-crit team would look something like this: + + .

Tldr: there is no wrong way to play the game, your time as f2p is not done as long as you don't want it to be, you do not necessarily "need" anything, especially when you already have Waver, Merlin and Tamamo, go for whichever banner, makes little difference, personally recommend assassin, though lancer works slightly better with Merlin.

Sorry if this was long af and a drain to read lol, dunno how to condense.

Not sure what you're worried about with that top tier line-up. I can't believe you're F2P with those servants, you're incredibly lucky. I had to spend a lot to get mine.
You can absolutely remain F2P and spend only on guaranteed gachas; you have the top 3 support Casters so you can build any team you want.
Can't really advise which banner, you don't NEED any top tiers to clear the content in this game. Roll for whoever you want really.

1. Only Jeanne at Jack are the only SSR in the Extra+Assassin GSSR that is permanent. Rolling on that banner could have a chance to roll a SR assassin.

2. Bond levels are factor in the Solomon. I'm using bond 10 NP2 Herc+Waver+double Merlin, all max skills. It can one-shot the pillar. Vlad's NP damage is average or below, but he will have his skill upgrade this year, thus increasing damage. Vlad isn't bad, I'm using him along with Waver and Da Vinci against assassin enemies.

Don't neglect your R and SR servants. Siegfried and Saberlot carried me through Babylon along with support Waver. I have no need for backline. Always utilize class advantage if possible. My normal setup is one ST, one AoE and one Waver.

3. There isn't really an arts crit team besides Nursery Rhyme, Saberlot and CasGil. You'll want arts crit for NP gain rather than the damage. Passive crit star gen like 2030 is vital to crit teams. But honestly, even when I run Jalter+Merlin+Waver in normal battles, I don't really care about crits. I just let the RNG do the crits for me. My gameplay style is in first wave, do normal damage. Second wave, proc Waver's defense. Third wave, annihilate all enemies with NP. It usually takes 6-7 turns overall.

Go with Lancer since those servants go well with Merlin and Waver. But the most ideal would be Rider servants especially Quetz and Ozy really go along with your supports.

I'm also F2P. As long as you are dedicated to the growth of your servants, nothing could really go wrong. After playing for a year, I have more than 40 max leveled servants with skills at 6/6/6 and SSR at 10/10/10 (except Da Vinci coz pages) but more or less 15 servants are utilized. Always clear the shop during events if you can, stack embers during lottery, farm QP, etc. FGO is a neverending grind.

You have the holy trinity of supports. You can do anything. If you do want to roll, either lancer or assassin banner will do.
A crit team utilies crit stars to do crit damage. A buster crit team uses the crits to do more damage on a buster card. An arts crit team uses an arts crit for more damage and more np charge. It is highly recommended to have a 2030 craft essence, a passive star genner like merlin, and a star absorbing dps like altera, gilgamesh, or iskandar.
You do not need any more gold servants. Get the free event ones and thats it.
Lancer for dps and assassin for a stargenner or hard staller.

You have so many SSRs and you think your F2P status is becoming unsustainable? Then what should plebs like me with two SSRs do? :P

One F/GO fundamental is to pay attention to class advantage. Instead of taking one of every class to quests, take the classes that have advantage over the enemies. The game usually tells you what classes you'll be fighting before you enter the quest.

Another fundamental is to bring supports, not just attackers. Most setups go Damage Dealer + Support + Support, or Damage Dealer + Sub Attacker + Support. An example of the former would be Vlad, Tamamo, and Waver, as you've discovered. An example of the latter would be something like Saberlot + Caster Gil + Hans (best for a mixed Lancer+Assassin node, though you can run it for pure Lancer nodes too). You /can/ run two main attackers together, but it's usually for quick nukage, and can become inefficient for longer fights. (Example of dual-attacker team: My team vs. Andromalius had both Chloe and Archuria in the front line, Waver charging Archuria's NP, CasGil for buffs, then Hans switched in with Combat Uniform for further buffs).

Don't worry if you can't one-shot the pillars. Most of those set-ups are not particularly F2P friendly (Bond 10 Jalter, NP2 Cu Alter, double Merlin ect.) Vlad+Tamamo+Merlin is still a plenty strong team for boss fights, just not ideal for one-shotting because Tamamo teams take a while to get going (her NP charge is tied to her own NP, compared to someone like Waver who charges on demand).

It's /good/ that each GSSR banner has few Servants inside. That increases the chance of getting the Servant you want. :) I might suggest Lancer for you, since all three are Merlin-compatible and all three are... actually Lancers. Rolling the Assassin banner could get you Jeanne, who is good for challenge quests but isn't a necessity when you have Merlin. But if you really want Jack and don't mind Jeanne, the Assassin banner is great too.