Replacing rigid fork with suspension fork Can I replace a rigid fork with a suspension fork on a Mongoose  Alder bike. 27.5 . 

If so, what particular forks? Under $100.00
Technically yes. You would need to get a fork with a straight steerer (looks like its standard 1 1/8") that was long enough for the frame, probably a 9mm QR dropout (although you wheel is a solid axle, not QR).  You would be best with a fork of 80 or 100mm travel or you would upset the bike geometry. 

However, a fork will probably cost as much as the bike, and a good fork that makes the upgrade worth while will cost twice as much. Unless you have a fork from a donor bike or lying around, its not worth it as it would be cheaper to buy a used bike with suspension.