>Question 1. What are the pros of TBHs?
Many have already been mentioned. But they are much easier to build. Can be built from scrap lumber (free). Are easy to work (no lifting supers). The bees stay calmer, because less of them are exposed (no gaps between the top bars). No foundation to buy or put in.
>Question 2. What are the cons of TBHs?
They require more frequent attention. You can't just walk off and leave them for months you have to keep an eye on things. If the comb starts getting off you'll need to take steps to straigtnen it. When it fills up you'll need to harvest a little now and then. A Langstroth you could throw a bunch of supers on in the spring and come back and harvest them in the fall. A TBH would have to be harvested several times to keep it from running out of room. If this is in your backyard this is not a problem. If the hive is 50 miles away, this IS a problem.
>Question 3 Will you give me a million dollars?
>how fast does it take the bees to start building comb - and the Queen to start laying eggs since there is no drawn out comb to start with?
There is no drawn comb in a langstroth either, unless you happen to have some on hand. They willd usually draw enough comb for the queen to start laying in in about three days. When the cells are only 1/4" deep the queen will lay in them and the workers will continue to draw them out.
> Does it take longer to get a hive established with a TBH?
> And should I feed - feed - feed these bees for comb production, or will there be enough with nectar flow to get them going?
That depends on your climate and your blooms. Here, right now, there is a flow. Not a major one, but they are more interested in the nectar than honey I have left out.
There are pictures and a little commentary on my web site on top bar hives and on natural cell size and foundationless (which top bars are).www.bushfarms.com