The leaves fall off because of rust. The air is just too humid in Houston. With all the rain, the problem is even more so this year. There is milky sap on the stem end when you pick the fruit because the fruit is not fully ripe yet. If you bought the trees at a nursery in Houston, there is not telling what you have. I say this with lots of experience. The more popular varieties around the Houston area are Celeste, Kadota, Alma, and Brown Turkey. You already said they do not turn brown, so we can eliminate BT. If your fruit stays yellow, then I would tend to agree with everyone else and say Kadota (or one of its variants). If your tree has tinges of golden brown, it is probably Alma. The fruit on your tree does not appear to be the same size/shape as the Celeste variant that seems to be everywhere in Houston. If you live close to the Clear Lake area, I can direct you to where a Celeste, an Alma, and a Brown Turkey live and hang over a fence in public view. You could go to those locations to see what they look like and what stage of development they are in. ~james

Most figs have two crops a year with one being lighter. If you live way up north or have a certain variety, you may only get one a year i.e. no figs this year then. Fig trees can sometimes just drop all figs and/or all leaves every so often. Nothing to really worry about as they will recover. What's that black pipe along that wall?

Your trees were pruned to be trees, not bushes. They appear to be at least 3 years old. Really hard to tell age because some trees are more vigorous than others. For instance, I had a Fig in a pot for two years, then planted it in ground. Suddenly that little thing trippled in size and it's trunk(s) became thick. Now it's huge, and I think nobody would guess it's only 4 years old. It's got about 15 figs per branch and there are a lot of branches. Every year, as your trees grow older, they will put out more figs. Really hard to know what a potted fig can produce. A lot depends on variety too. I don't have LSU Purple, but my Celeste is very productive. At 2 years old, it has about 20 figs, but it's still in it's pot and has worked it's way into the ground. This year when it's dormant, it will be planted in ground. You'll just have to be patient and wait. The figs will come. We get mild snow fluries here in winter maybe for a day or two, so planting in containers isn't important, but many who live where it snows have to bring their containers in for protection from freeze. I know you rent so want to take them with you. Good plan! :-)

If a tree is grown from Tissue Cultured apical meristems, it is possible to have a 100% virus free variety. However viruses can be spread by fig mites and unless someone is scrupulous about only growing tissue cultured figs and keeping the collection free of mites, it is only a matter of time before that variety is also infected. Most collectors don't seem to care too much about viruses because nearly all fig varieties seem to produce reasonably well despite having strong evidence of various types of viruses. A commercial grower on the other hand might prefer varieties that are completely virus free for maximum productivity. This is where tissue culture might have huge benefit. The technology isn't particularly novel or difficult so I am wondering why the demand isnt there. I am hypothesizing that perhaps the productivity of trees isn't that badly affected at least for the commercially successful varieties. Now if I could only get someone to culture a virus free Ischia Black - USDA for me. I am happy to provide cuttings!