Background Check Questions

I have recently sent information about past employment and education for a background check for a prospective job, and I have not done anything I would expect to disqualify me (e.g. I have never had any legal trouble, not even a parking ticket, I have evidence of each of my past jobs and degrees such as contracts and payslips, I have never gone bankrupt, I have never defaulted on a loan...), but there are two things I am worried about:

1. I was furloughed from my last job because of COVID (I explained this, and also explained what I have been doing in the meantime), and since I graduated from a Master's degree, I have not been in employment or education, and I have tried applying for many companies but this is the first one to give me an interview. The background check company asked me to explain the gap in employment from the end of my degree to the present, and although I did a training course and applied for the aforementioned prospective job, the only job search related evidence they are interested in is proof of interviews. Will my lack of success with other jobs because of COVID be held against me?
2. Some of my past employers no longer work at those companies, so I have no contact details for them. I do have an email and phone for my previous boss, and he still works at the company I was last at, so I included those. I do however have payslips for those jobs, and a P45 and contract for one of them. Will the fact that I cannot get contact info for people who have left the companies I worked at affect me? Should I explain to the background check company that my previous employers have left their companies and I have no contact info for them, and provide my other evidence of employment?

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