Why would 3 prong plugs not fit into 3 prong outlets. This is a new home. All outlets only work on 2 prong plugs.?

This is very strange indeed. All modern houses in USA would have 3-prong outlets. I can't see how it could pass an electrical inspection. Check with the local agency who does inspections. Check your electric panel and look for an inspection sticker.

I have encountered receptacles that are very hard to use because one or more of the pin slots (I don't know what else to call them) are way too tight. There is no easy remedy for this problem except to press hard to get the plug into the receptacle or replace the receptacle with one of a better quality.

There are also child protective receptacles that require that two or three of the pins be pressed in at the same time or none of them will go. If the plug is just slightly off true it won't go.