Do I need any gaskets or hardware to install this?

You'll need fresh exhaust gaskets at the manifold and downpipe flanges — don't reuse old ones. Existing factory bolts typically work, but pick up new hardware to be safe; they're cheap insurance against leaks.

Will my check engine light clear once this is installed?

Installation alone won't clear a stored code. After you bolt it on and run the engine, the vehicle's computer will run its diagnostic cycle over the next 50–100 miles of normal driving. If the converter is good and no other issues exist, the light should turn off on its own.

Can I install this myself with basic tools?

Yes — you need jack stands, a wrench set, maybe a oxygen sensor socket if you're pulling the old one. The trickiest part is usually access; give yourself a couple hours and you're done.