I found leak right under the muffler so I took a look at it. As you can see from pictures, it looks like it’s burned out? Any advice?

 

Thats just condensation no worries . Alot of mufflers have a hole there for just this reason.

 

Mine too, same hole, same place. Just there to let the condensation dribble out, don't worry about it.

 

A gasoline burning engine produces quite a bit of water when the fuel burns. USUALLY the exhaust system is hot enough to keep the water in steam form so it simply exits the exhaust with the burned fuel.

On cold start or short trips, the exhaust system cannot get hot enough to keep the water as steam. So, all mufflers have a hole somewhere or a loose seam that the water can drip from.

This leads to all sorts of interesting problems. The water picks up all sorts of NASTY chemicals from the combustion process and can dissolve the metal that the exhaust system is made of.

Stainless exhaust systems help with the corrosion, but even stainless steel will lose against the water eventually.

That's why there are still muffler shops around.