If your IP changes, you need to specify it in your account on M2E client's portal. Tick 'remember my choice' option so that every new IP can be automatically added to your license. In this way, the license will not be going invalid and the synch will not be interrupted.
M2E always updates the Products on eBay based on the Magento values. And if product is sold out on my website, M2E always stops it on eBay as well. It might be that you're updating Magento product quantities with some third-party tool. In this case, you need to adjust it properly so M2E can see the changes made to your products quantities.
Here, check this article: https://docs.m2epro.com/display/BestPracticeMagento2/Programmatic+Possibilities+to+work+with+Extension