Leak/s in top floor flat ceiling- offer made subject to these being fixed by exchange of contracts

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I've made an offer to purchase a privately owned  top floor (4th floor) ex local authority flat where the lease is owned by the council.

As I went to the property with a builder prior to making the offer, we noticed damp marks in bedroom 1 ceiling, a wet wall and ceiling corner in bedroom 2 (expanding to bedroom 3 corner) and black mould marks in the bathroom ceiling and  a crack in the kitchen ceiling.

I made my offer subject to the obvious leak being fixed (which seemed to come from a pipe outside on the building wall) and the ceiling crack in kitchen and damp marks in bedroom 1 ceiling being investigated and fixed.

The estate agent reported these to the council who will come and investigate above issues within 7 days and will then follow up what to fix. At the moment I'm out of UK as I just found out I've lost my relative and cannot therefore be present during any of these investigations, which really bothers me. I very much want to go ahead with purchasing this flat, however having heard all the horror stories of 'bad' freeholders i.e. the council here and management companies, I'm very wary of going ahead.

Initially I insisted from the estate agent who deals with the seller's solicitor (no contact with seller itself) that I want to have all those problems fixed before completing, also I want the council to repair the affected wall and ceiling inside the 2 bedrooms. I said I want written confirmation from the council what exactly they'll fix and when they’ll fix them.

How can I know for certain that they will fix them PROPERLY, and within the timeline before exchanging contracts?  I said to the estate agent I do not want to incur any costs (surveyor or solicitor) before I have guarantee that the problems will get fixed and when they'll get fixed  (and the leak/s would come up in the survey in any case).

I'm very worried about this, as I'm not present there myself and also as I don't know how to trust that the leak/s and the roof will get fixed PERMANENTLY and not with a temporary fix (as I've repeatedly now read from these blogs) and the flat will actually be a safe home to live in.

Should I actully pay for a surveyor to assess the initial problem, to compare that to the council opinion and if they  both agree with each others, ask for a written confirmation and timeline of the repairs from council (freeholder) and then ask in the end my surveyor to check the work again before exchanging the contracts?

Please help with how to proceed safely with this purchase, or whether it's wise to proceed at all??

Thank you in advance!