I haven't checked lately, but IIRC, the only difference between free and paid versions of Osmand is that the paid version gives you unlimited map downloads. In the US, each state is one map, so if you only have a handful of states you need then you can get by with the free version.

Yes, I have exported routes from MMR and used them in Osmand. I haven't used the turn-by-turn directions feature with bike routes, but others have reported it works.

I've found that Osmand isn't the best at computing routes, where you start at X and just want to it to tell you how to get to Y. The routes it picks sometimes seem to be less logical than, for example, the dedicated Tom Tom GPS I use in the car. It does have a bike navigation mode though, so if you're biking and there is a bike path on the route, it will pick that vs a road.