I have a Trek 720 multitrack with Shimano 200CX rear deraileur & 12 to 28 tooth sprocket set that I wanted to convert from twistgrip shifter to lever style. Will Shimano STX M037 rapid fire shifters work with what I have?

Match the number of gears in the shifter to the number of sprockets on the freewheel/cassette. For example, 7-speed.

My cassette is a 7-speed & so is the shifter I'm asking about. The reason I ask is that I got a SRAM TRX 7-speed trigger shifter that doesn't work-skips over 2 gears from 1 shift click & stcks in 1st & 2nd-and I'm sure it's a compatability issue because I sent the 1st one I got back as a defect and the replacement was as bad as the 1st one. Point being it seems like there's more to it than simply matching 7 to 7.

I was going to mention that most SRAM rear shifters are not compatible with Shimano rear derailleurs. However, there are a few SRAM shifters that are Shimano-compatible and it looks like the TRX is one of those.

The original grip-shifters, SRAM TRX, and Shimano shifters should all be interchangable.

I would double-check that you have installed the new shifter and adjusted the rear derailleur correctly.

What do you mean by "stcks in 1st & 2nd"?

sram uses a 1:1 pull ratio while shimano uses a 2:1 which perfectly explains your problem. I believe the SRAM Attack shifter will work, its an 8 speed shifter, but you can use the limit screw on your rear derailleur to stop the shifter from shifting into a ghost 8th gear