Can I freely go between conquest mode and normal, or will it reset my normal?

[Zixky]

ie should i do all the side stuff on normal first

[astrofelix59]

You can swap between no problem, don't have to do missions in order.

[Predator.]

the game literally tells you it will save your progress, look closely at the screen where you are asked if you are sure. Ubisoft isn't great at making these things obvious, they sort of bury things in busy screens and obscure places.