@Reposter1. Did the New Republic totally use only Rebel Starfighters? Does this mean X-wings, A-Wings and Y-wings are the standard for the New Republic Fleets? Why not use Imperial Technology like TIE Fighters to mix into their fleets if they got captured?
They either scrapped Imperial TIEs, and/or put them into Project Starhawk. The New Republic ships were better in terms of life support and shields - they were more humane to use, so thus they were used; unlike the empire who didn't care much for their pilots
2. What does the New Republic army have as combat Armour for their Infantry men? Did the New Republic appropriate Imperium Stormtrooper Armour into their army after the Empire lost in Return Of The Jedi?
No. They scrapped it for Starhawk and already had their own good armour. Most of their military was scraped soon after Endor and Jakku anyway.
3. Did the New Republic capture any Imperial Star Destroyers? Why not use them for the New Republic Fleet as well?
They were scrapped into Project Starhawk. Same things as before.