Hey! I'll be studying a PGCE in secondary English and I had a gap from September 2020-November 2021 that showed on my application and caused me no issues at all so I wouldn't worry about the gap causing any issues. My teacher training advisor told me that often they ask about gaps in employment etc as a safeguarding question in case candidates were perhaps in prison etc.
In terms of your mental health, there are two schools of thought in terms of mentioning this to providers when applying for a course or submitting a fitness to teach assessment after you've received an offer for example. Some people are scared to say that have a mental health issue in case they are judged unable to teach. Although there is no list of conditions that bar you from teaching, providers have to have reasonable belief that any mental health problems you have won't cause any safe guarding issues or be worsened by being in a school environment. From what I've read about it, if you have an MH condition and are receiving treatment that works and helps to mange the condition etc then mentioning this shouldn't have an adverse effect. You can be entitled to additional support for your condition too which many people feel is worth getting so they disclose their MH history.
Hope this helps!