The Chef's Table books 180 days out (it never booked 1-2 years out). Also, I think it never is available for Wednesday or Friday nights, but you can call and doublecheck that.
It can be for the two of you. It is a great experience if you are into food and wine. If you are looking for a romantic evening out, I think the dining room is the better choice -- just my opinion, though. The dining room is very luxurious and romantic, with roomy tables, wonderful service and a harpist. The Chef's Table is in an alcove off the kitchen. You see the chefs preparing the evening's meals. The service is wonderful and the interaction with the chefs is fun. But, it's not really romantic.
DH and I have done the Chef's Table 5 or 6 times and will be doing it again next month. We love it. But, you should be something of a foodie or it may not be worth the price. You can tell the chef to hold the foie gras, the caviar, etc. if you don't like those things, but then you're kind of overpaying, IMO.
Look at the menus for V&A dining room. The Chef's Table offers the same choices -- you just get more courses and more opportunities to taste most everything featured on the menu that evening.