Answers

Cannot recommend anyone, but it sounds like the door needs to be puled out and make the rough opening bigger. re-install door.

You should check with a structural engineer for this one. Most good lumber yards or a steel supply warehouse have one on staff.

This sounds pretty major. I would get a structural engineer in to give recommendations. If there are any logs that are rotten around the perimeter you should have them replaced right away. Call ryan at 877-788-5647 for help.

Contact ryan at 877-788-5643 or ryan@logrepair.com for help

You may, but if you are only going a few inches you should be good. If you can get your hands on a metal detector it may help.

You should replace them with logs to maintain the quality of the home. Call Ryan at 877-788-5647 for help.

Maybe caulk the inside on the north. Hopefully you put some foam board under the siding to help insulate.

You should call Ryan at 877-788-5647. He can help with cost estimate.

I’m not sure what pcp is. You might mean cca which is the chemical used to treat wood mostly for utility poles. I think there is a very slight chance that there would be cca’s in the logs unless you know the previous owner was treating it with creosote.

Sounds like it wasn’t dried properly before being installed. I would be afraid of gluing it like you want for fear that it may cause it to split in the middle of the board. You may want to put a humidifier in the room to slow down the drying.