Can I safely drive 2hrs on a dragging muffler

Question edited for clarity and add some full stops and commas and stuff. That was one of the longest run-on sentences!
Question moved to model category.

Yes, the wires are probably from the o2 sensors on the Catalytic Converter but really could be from anything. Reconnecting them should fix the starting issue.

Have the front end checked out for loose parts. have a wheel alignment done to correct castor wobble

Sounds like your timing belt jumped a tooth or two. Any idea how long it's been since it was replaced ?

Its possibly the heat shield on either the catalytic converter or the muffler is loose. It could be something a small as a hubcap being loose as well.

most likely you drive by a dozen muffler shops every day. stop at one of them and for free they will look at it and tell you what is wrong with it and how much to fix.

Take your car to a muffler shop and ask them if it's possible to reweld the exhaust pipe to the muffler. If the exhaust has rusted too thin, they wont be able to weld it safely, at that point you will have to replace the entire system unfortunately. Exhaust systems comes in sections, so ask them if its possible for them to replace the exhaust from the catalytic converter back only. It should be cheaper if they can do that. Good luck!

You can fix this until you get the parts by using a wire hanger. The part that broke is called the muffler hanger. Not a big deal and is an easy fix. You don't have to buy anything spectacular if you don't want to. It is just to support the muffler/exhaust.

Now, did the muffler get the hole in it or did the catalytic converter get it?

You should be okay for short trips . I think the muffler went out has a hole or leak.
The noise is going to get louder and louder if it is the muffler.

Yes, it will cause you no problems. Just avoid excessively long idling.