Can I use an "8 speed compatible" crank such as Shimano FC-2303 with a 7 speed Shimano MF-HG37 freewheel? I have a 2004 Giant Cypress I use for commuting, and the entire drivetrain is very worn out (shark teeth and chipped teeth, front and back).  I need to replace the Shimano MF-TZ20 7-speed (14-34t) freewheel, chain (I know to enough to always replace the chain when replacing the freewheel!), and Shimano M131 (48/38/28t) crankset (not just the chain rings, unfortunately, because they're riveted on this cheap crankset)-:

I have a very flat commute and would like a taller top gear, so I'm thinking of using an MF-HG37 (13-28t) freewheel in back (since I never need the 34 rear gear on my ride anyway), and that seems like a straightforward substitution.

What I'm really wondering about is whether I can increase my top gear further by using a crankset such as the FC-2303 (52/40/30).  Shimano says it is "8 speed compatible", and I know 8 speed chains are the same width as 7 speed chains, so it seems like it should be OK.  Can anybody set me straight for sure?

Thanks.
The FC-2303 is a non series road crank set. It will work, with some shifting degradation, but it is not an ideal match. 

8 speed road shifters, and 8 speed mountain shifters pull a different amount of cable, because the spacing of the chain rings on a road crank is different than that on a mountain crank set. 

If you want it to work well, you need to also change your front derailleur, and front shifter. Depending on your bike and the direction of cable pull, you may or may not be able to put a road dérailleur on it, but you can get a touring dérailleur. And you'll need an 8 speed flat bar road shifter which will pull the correct amount of cable for for an 8 speed road crank set.