There is a distinct rattle when starting my car and hitting the gas

Unfortunately, we need to separate these issues out into separate posts. The only reason we need to is because others will not find the answers to the other issues. So let's address the rattling noise here and get a new post started for the other issues.

The rattling noise is most likely an exhaust issue but I would not secure this to the body or frame. Your exhaust needs to be isolated by rubber hangers from the frame and body because it will vibrate and cause all sorts of other noise issues.

So the way to try and find this is to use a rubber hammer and hit the exhaust to see where it is rattling. If you can't locate it then it is most likely the interior portions of the converters or muffler.

Let me know if you have questions and what you find and we can go from there. If this does not sound right then can you get a video of the noise so we can get on the same page? Thanks

Exhaust rattles that sound like pebbles hitting tin are commonly the heat shields. For those you can put the vehicle up in the air and look and feel of the shields, some are attached to the exhaust and some to the car, you would just reattach them if loose, for instance if it's one attached to the body and it rusted enough to fall free, remove the bolt or screw and use a fender washer to repair it. If it's one attached to the converter or similar it's a bit harder as the factory ones are usually welded in place to the pipe. For those a quick zap with a MIG welder usually works. If you don't have one most shops could tack it back in place.

As for the other two questions, please ask them as separate items, we try to keep issues within a single topic to make it easier to follow the problem, plus you can get more people on a question. Thank you.