I have an Inspiron 1525 with a Celron 540 1.8Ghz CPU. I'd like to upgrade to a faster CPU and was wondering whether the T7300 or T6400 are compatible with my motherboard and which one I should get.

Your Celeron 540 is based on the original Core 2 Duo architecture, code name "Merom".   Here's a list of all "Merom" processors on the Intel website- http://ark.intel.com/ProductCollection.aspx?codeName=2683

Any of those should work well.  The T7500 was one of the better Merom chips, the T7700 even better.