Do I need new bolts when I install this gasket?

The gasket itself is the wear item—bolts can be reused if they're in good condition. Inspect them before reassembly; if they're corroded or stripped, grab a new set of header bolts rated for exhaust temperatures.

Should I use any sealer or adhesive with this gasket?

No—this gasket is designed to seal under bolt pressure alone. Apply a light coat of anti-seize compound to the bolt threads to prevent corrosion and make future removal easier, but keep sealer away from the gasket face itself.

Will this stop an existing exhaust leak at the header?

Yes, if the leak is coming from the header-to-head joint. If the manifold itself is cracked or warped, no gasket will fix it—you'll need to address the underlying damage first.