It's difficult to say without knowing anything about the property or the circumstances as to why it's empty. For example, freehold, freehold with man co, leasehold, divorcing couple, probate property, second property, ex-rental etc.
The 14 weeks delay caused by the sellers is unfortunate, but the legal work still has to be done correctly and will only have started from when the draft contract paperwork was received by your solicitor.
Enquiries can take a long time. The seller's solicitor will need to refer a lot of the enquiries made by your solicitor to third parties, including your seller. Do you know if the seller has simply moved out of the property, are they acting as Executor for the owner who has passed away, or has the owner gone into a care home? Etc, etc.
Your solicitor does need to review the responses he receives before deciding whether he needs to raise additional enquiries for further clarification, i.e. a second round of enquiries to be made. If the responses are satisfactory, your solicitor will then compile a report on title to send to you.
The report on title will contain information about the property, together with documents for your signature. You should read this carefully before sending back signed documents to confirm that you are happy to proceed. After the solicitor receives the signed documents back, they will then start to discuss dates with you and the other side.
I would probably say that your timeline is tight, but without knowing how far along you are with the legal work, I wouldn't want to guess.
The EA, while trying to be helpful, is not involved with the legal work, so won't really know what still needs to be done or how long it will take. Their involvement once a sale is agreed is mainly to keep everyone happy and to smooth over any frustrations.