Samsung Infuse is getting really hot when using a Samsung wall charger that came with Samsung Strive. Is this bad? The output specifications for the Samsung Strive charger match those of the Samsung Infuse charger, so I don't see why the phone is heating up so much.

Also, when charging the Samsung Infuse with this non-stock charger (although it is still made by samsung) while the phone is off, the charging never stops. The display never says (100%) even after a full night of charging. The animated dots keep on moving as if the phone is still charging.

Is all this bad or are we ok here? I wouldn't want to blow a fuse in the brand new Infuse!
The phone should be correctly detecting the charge of the battery even if the charger isn't right.  So it sounds to me more like a phone problem.  Either way I would discontinue this ... if the phone really is trying to charge the battery past its limit you could definitely fry the battery or your device.

Did you ever have an Infuse charger, and if so did it work?

You could try running the battery dry and then charging from that state; I've heard that can help when the battery stats get messed up.  In conjunction you could wipe the battery stats (you'll have to Google how to do that for the Infuse) but that's generally a last resort since it takes quite a few charge cycles for the battery stats to get rebuilt (your phone relies on them to determine the charge of your battery with any accuracy).