Hi, congrats on your wedding, I'm sure you will have a wonderful honeymoon in Bali and Lombok
You will not be able to book tickets late at night at the domestic terminal - all the airline offices close around 4.30 - 5pm for ticket sales. You will be able to either get the Jayakarta to organise the tickets for you, or use a local agent in Legian to do it, or take a trip back out to the airport to do yourself the next day. It only costs a little more to use an agent to do it (less than $10) so if it was me, I would be doing that and enjoying your honeymoon in more pleasant pursuits.
There are 3 airlines that go at the moment, and they are all much the same. I wouldn't recommend one over the other.
I haven't stayed at the Beach House so can't comment personally.
The transfer to pick you up at Lombok airport and transfer you to Gili T by speedboat is not an unreasonable price. The alternative is the cost of a taxi to Bangsal Harbour for around Rp 100,000 and then you have to run the gauntlet of the very aggressive touts, and then the transfer itself on a small boat is around another Rp 30,000 each (and you will have to wait for the boat to fill). If you get to Bangsal too late, you may have to charter a boat to take you, and that will cost you as much as what you would have paid for the speed boat + hassle. While the latter option may be a bit cheaper, for the little extra the Beach House transfer would cost it would be be my preference, particularly as you are on your honeymoon. Getting picked up at the airport and whisked off to Gili T by speedboat is a much more pleasurable experience!
Can't comment on website booking for rate - do you mean as opposed to just turning up and trying for the best rate then?
Have a lovely time