You actually have a very nice range of servants, although a lot of them are underleveled. I’d really suggest getting some of them up to max level instead of spreading out your EXP that much.
As for the boss fights, Lancer is easy. You shouldn’t have any trouble with him at all.
You don’t have any good single target casters, so use Mecha Eli against assassin. She should be able to do a huge chunk of damage for you.
Archer isn’t that tough as long as you can keep the burns under control. You’re definitely going to want Medea Lily. As for your DPS, I think I beat it with either Karna or Lalter. My Lalter is NP5 though (not deliberate, Merlin decided to evade me), so you might have more success with Santa Jeanne.
Rider/Berserker is by far the hardest fight in the singularity. Try to burst it down as quickly as you can with either Kiara or Scathsassin.
The big ghost was just a big ghost. Fairly easy.
Saber only takes damage from NPs, so you’ll have to use strong archers. Santilla is great, and if you can throw some exp at Euryale, you won’t regret it.
Against Avenger you can choose your own supports again, so you’re fine.
Obviously in all of these fights, Waver, Mash, and Hans are your best friends.