Since the university presumably has some input, e.g., through discussions with your supervisor (because otherwise, it would be independent research, not a Ph.D. project), the university will at least have a reasonable claim on IP.
We can't tell you. You will need to talk to your employer's legal and/or Human Resources team, and get them in contact with the university. There may be policies on situations like these on one of the two sides which the other side is happy about; then things may be easy. There may be policies on both sides, then negotiations may ensue. This may take a while.
As an example, if I collaborate with a university on some research project, my employer typically wants to own all IP generated, but will license it back to the university involved for research purposes at no cost. If the university is fine with that, they can just sign our contract, and everyone is happy. If they are not, things get tricky.
Whatever you do, start soon. I have been quoted a six month time frame for such negotiations from my employer's legal team. Also, note that if more than one university is involved, e.g., in some research collaboration, the negotiations may become very involved - I personally have been counseled not to even try a constellation like this, because coming to an agreement is likely impossible.