I guess since you didn't say more it's hard to tell, but how did you decide on this TA? Was it a recommendation from a friend? Another chatroom? Ignoring an email, or a request would indicate to me that they weren't interested in my business, was either too busy, or too lazy to do it, or had some type of emergency where they couldn't respond.
From my experience I get a confirmation as soon as I say let's do it, and generally a hold is placed while I'm thinking about it. Once money is actually on the table I get another confirmation showing that. Anytime there is any type of change at all I get a new invoice showing that. It's not uncommon, depending on how long in advance I make a booking, to have between 3-8 invoices during the life of a booking.