Ok from the photos I think I would tentatively conclude the followings:
1. The BB is a traditional cup and cone one.
If it needs to be replaced (because e.g. the cup is pitted, or a new chainset's requirement) then a C spanner and Sheldon's nut & bolt tool are needed. The use of the former to remove the adjustable cup is usually possible unless the cup is made of cheese, the use of the latter on the fixed cup could require some swearing...
2. From the photo that shows part of the chainrings I can't see any broken or obviously shark tooth shaped teeth, and the chainset does not look too bad to me to warrant immediate replacement. But if you have bought a replacement already I would say keep it just in case.
3. The photos aren't close up enough for me to be sure you have a Shimano splined freewheel. I wonder if you could check to see if it appears to have matching slots for this?
So perhaps the other question remains is whether the existing BB runs smoothly without play (when the chain is off the chainset) or not.
Sheldon's fixed cup nut and bolt tool description:
http://www.sheldonbrown.com/tooltips/bbcups.html