Question about next steps

Hi! We toured and placed an offer on a home last weekend & had an inspection clause in there. Seller countered & asked we shorten the window so our inspection took place on Tuesday - results in full Thursday - submitted updated offer Thursday (lowered price and requested they fix some major health safety hazard stuff prior to move in) - they countered & we re-countered and they’re fixing everything and have agreed to our price and we signed the amended purchase agreement.

Earnest money was sent during the inspection window, but what now? Everything is signed by both us and the sellers - is the sale final if they fix everything prior to our closing date(which is in just about a month from today, they wanted a quick close) and monetary stuff goes through? Are there more things that need to be done and completed? When will we know that the house will for sure be ours on closing date?

Thank you in advance! I tried reading articles but none placed everything in an order that worked with how our process has gone so far and I don’t want to get too excited if I shouldn’t just yet!