You would need to find a civil litigation attorney, typically a breach of contract attorney.
The previous owner could be at fault if they knew about the issues and failed to disclose them. The inspector also if he should have seen the problem during the inspection and also did not disclose it.
Yes, you insurance company would still be responsible for covering the contents, they would just subrogate the claim against the HOA and their insurance company (meaning they would then sue the HOA and their insurance company for the amount they had to pay you).
It depends on the types of repairs you would need to make to your unit. If you can remain in the unit while the repairs are made, the Board wouldn't be obligated to do so. However, if you need to leave the property to make the repairs, then they would.
There is no law stating that they have a specific time limit within which to fix the property.
You would not be suing yourself because you will be suing the Association for negligence. They have insurance that covers them for that. It is separate from any unit owners in the building. You would be suing the Association, the Board, and their insurance company.
It depends on how much they want to fight the case. Typical litigation can take anywhere from 6 months to 2 years. Sometimes, these claims can be resolved quicker. It all depends on what the Association's position is on the repairs and what their responsibility is.