Home Improvement Questions? Ask a Handyman for Answers
I see you have basically listed your question with more concerns. The fact that a door is not operating properly is definately a cause for concern and an early warning that there
could be more serious problems to come. Some may tell you the door is just reacting to moisture or humidity and that could be true; however whithvall that is going on around your home this is no time to sevond guess.
I would have a Registered Certified Structural Engineer inspect your home and foundation as soon as possible.
If their report is negative and calls for action on the part of your neighbors construction you beed to present a copy to them , the local inspectors and your home owners insurance adjuster. You fo not beed anyones permission to do this.
You may even be able to recover the cost of hiring the engineer. The ibspections department will notify the neighbors contractors of the need for additional permits and work if that is deemed necessary by your engineer.
Doing this puts professionals behind your concerns with factual information.
I would do this as soon as possible.