Shimano SL-M310 or SRAM TRX are two trigger options that would match your rear cogs. The TRX is one of the few SRAM shifters that matches shimano derailleurs and is, to my knowledge, the only SRAM trigger option to do so. Either appear to run near $30.

Providing you don't ride a chain beyond reasonable wear (1%), rear cogs can last through two or more chains. But continuing to ride a worn chain will quickly wear the rear cogs. If in doubt, measure your chain with a ruler.

The chain used on your 7sp is the same size as all chains used on 6, 7 & 8 speed drivetrains. They're inexpensive and last a long time.

I suspect you actually have a cassette, not a freewheel. If you do have a cassette, there's a great chance that it's mounted on a 8/9/10 speed freehub body with a 4.5mm spacer behind the largest cog. Some people would use this as an opportunity to upgrade their drivetrain. An 8 sp cassette with narrower spacing (12-23, 12-25, 13-26) would allow much easier transitions between gear ratios and make better use of your triple crankset. Of course, you'd need 8sp shifters and cassette. The cassettes are less than $30, and you can pick up Shimano Alivio M410 rapid fire shifters for just over $30 online. And you'd need a new chain, since you always want to replace the chain when installing a new cassette.

Just food for thought. Not trying to encourage you to sspend money.