When buying a flat, it can be a stressful experience having your purchase delayed due to a hold up from someone else. Unfortunately, as you are not the leaseholder yet, you are not in a legal relationship with the landlord.
In this situation, there is nothing your solicitor can do to force the landlord to reply to these enquiries. The best thing you can do is ask your solicitor to continue to chase the landlord as this will put pressure on them to provide the answers.