Maybe exhaust issue

This sounds like multiple issues. The vehicle being louder while accelerating is most likely the exhaust has a hole in it. The only way to find this out is to visually inspect it where it sounds the loudest.

As for the running rough and stalling issue that sounds like a vacuum leak so here is a guide that will help with that. However, if you need more help with this issue we need to get a new post started because we need to keep each one to one topic. So let's keep this one on the exhaust issue.

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

The heat blowing on the floor sounds like a possible blend door issue in the HVAC system but again this would be another issue so we need too get a post started for that one.

Basically, we just need to keep each post to one issue and the one that is listed on the heading. There are two main reasons for this. First, it is easier to work on one issue at a time. Second, others will not find these issues that are not listed under the heading if they have the same one.

Sorry for any inconvenience but let me know what you find with the exhaust. Maybe get a video of it idling so we can hear it and then rev it up. A failed exhaust has a distinct sound so we will be able to determine if that is it just by hearing it. Then we just have to find the location of the leak.