I have few silly questions, please don't add any spoilers here. Keep it simple!

So I wonder if the perks you pick on Archery will effect your Conjuration Bow, if the Conjuration weapons will mix well with Archery and Sneak perks?
Such as you summon your Conjuration bow and you have perks on Archery that you zoom, will you then zoom?

And another question, just say yes or no. No spoilers please!
Would you say Sneak, Illusion, Conjuration, Archery is a good start to be a Stealth Mage Assassin?

Or would you say drop Sneak perks and focus on Illusion for "stealth"? Sorry for the tricky questions.

On your mage assassin question, I'd say go for Sneak first (15x damage on daggers specifically, the noise thing can be covered a bit by an illusion spell "Muffle", but you don't get any invisibility spells at first) - then the silent casting from Illusion, and Destruction runes / Conjuration summoning distances.

Didn't get silent casting yet so can't say whether it works well or not, but having a trap ready for when the fights unevitably break out in full rooms should be good.

3 points in Sneaking would seem the minimum to get to the bow Perk... I would say.
But even 4 is worth it for the Assasin's Blade Perk, can't go wrong for an assassin to take that one imho mage assassin or regular kind!