to answer your questions in the short, yes...
1- Using JavaScript it can be done easy enough. I have very good experience combining PHP and JS.
2- This can be handled using simple coding logic that is based on the success of the mail being sent.
3- Should be straight forward, but I would want to see where the count is stored. I would suspect in the MySQL db and is most likely in one table as an incremental counter. If it is based on a query of the number emails sent and recorded then you will need to make changes to the table structure and add a new query, or two. For me this is not an issue, it just need to be examined so the best solution is found and implemented.