What do you do with marie antoinette??

She’s a good survivor, np damage is bad but it’s has a aoe heal. If you have more than one of her burn her

she's a tank. Her NP removes all debuffs and heals your team but other than that she hits like paper

1st question answer, she is a sustained DPS + Anti-Male + AOE wave clearer and farmer, bonus she can clear debuff. Good for challenge quest and harder contents.
She's also a pretty strong solo servant.

2nd question answer, Stall team and daily farming team or Quick team is a good way to utilize her. Her main kit is her survivability, not her damage and she's similiar to OG Chu in terms of gameplay.
Vs male Zerker, bring two Marie Antoinette Rider plus one Euryale and you can kill almost any male bosses.
Or even 3 Marie if you've all of her version.

3rd question answer, it depend on you. If you're a total F2P it's not really recommended to burn Gold servants before they reach NP 5.

Bonus : i've played many kind of team playstyles, i can even make her into a boss killer. Servants is like a tool for you, you're the brain that control them.

She is basically a rider version of Cu Chulainn. However, she is less selfish than Cu as she can provide heals to the team and herself. Useful either for challenging quests, or if you don't have many strong offensive servants yet and need to rely on defensive skills.