Stuck on the first stage of Camelot, how to progress?

Looks to me like you'll need to take advantage of the 1/2 AP Ember farming to level your Servants.

I recommend leveling and ascending Robin Hood, Euryale, David, Cu Chulainn, and Lu Bu.

The first three are extremely helpful against the large number of Saber bosses in later stages, as well as Saber mobs. Cu for the Archers. Lu Bu, if you pair him with Mash and your friend's Merlin for durability and survivability, can deal massive amounts of damage to pretty any boss.

Leonidas and Georgios could also help for defensive play given their durability and taunt skills, much like Mash.

Do you have any embers in stock? Today's 1/2 AP ember is a good opportunity to raise your servants.

If you want to continue doing singularities, I suggest pick a damage dealer from your friends and field them with Mash and Hans.

Take a pause, go farm embers, they are 1/2 AP cost now. You can't beat Camelot with just that.

Raise your Silver Archers, also, Caesar, as there are 2 bosses weak to sabers (one which is archer...yes, bullshit, but true).

Be prepared to learn how to stall, Gawain has 80% dmg reduction, and charges the bar 2 times per turn, is AOE NP. David AOE Evade and Euryale double charm will be useful, more than most 5*.

Mordred does AOE NP EVERY turn. Have evades and stuns in your Archers. Also, she clear debuffs.

Lancelot has saber icon, but when you fight him, he's ruler class affinities. Just Grab a support Jalter and roast him.

Final boss pierce invulnerability and evade in her AOE NP, who is powerful as hell.

Good news, next singularity is much easier than this!

I cleared my way up to lostbelt 1 with using cu alter/herc support, lvl 1 mash and lvl 55 leonidas for almost every fight, and only used a couple command seals in total (Gawain and ushiwakamaru clones iirc). I suggest leveling a good taunter or two and you should be able to get carried by supports all the way

The way I cleared Camelot (and Babylon) was to have max level Hans, Georgios, and Mash. A friend support like Merlin or Waver does you no good if you don't have good damage servants to support, and while I did have Robin, Ushi, Jack, Caesar, and Cu, it's much better to use a friend's Ozy or Gil or Lancelot or bond 10 Herc if I really wanted to rack up the damage. Especially with the gimmicky bosses.

Also, I looked at every fight and played it like a bridge hand :) I tried to stack class advantage where I could, and planned out the fight in my head as to when someone was likely to die, or when I might swap in a backline to avoid class disadvantage but still have time to charge the NP before the final boss.

How to progress ? It's simple, pause for a while, build some solid party member, raise your favorite servant and then you're good to go ( 1/2 AP Ember farming is one of the best way to do this ).

After Camelot, Babylonia need at least some decent leveled servants to help clear it.

Instead of borrowing friend Merlin, it would be more efficient to borrow a friend damage dealer of the appropriate class and use your own supports (Hans and/or Mash).

I also suggest farming embers (half AP right now!) and levelling more Servants. Since you're already working on them, maxing out Hans, Kogil, Nursery Rhyme, Astolfo, ect. wouldn't be a bad idea (Hans is invaluable, and the rest of them will at least whittle down some Saber/Assassin/Caster mooks). You might want to level one of the ST Archers for the boss fights: Euryale for charm, Robin for damage, or David for his team-wide Evade.