In TX your zone doesn't matter for apple trees. Chilling does make a difference and soil drainage makes a huge difference. Short term flooding is OK, a day or two in summer. But combined with soil that drains poorly, flooding for very long can kill fruit trees. Planting on a berm can help a lot.

Have you considered growing water lilies??? haha. Seriously, goodluck with your weather! Try doing the best you can with varieties that do good in your heat. I think that may be your biggest challenge. http://planthardiness.ars.usda.gov/PHZMWeb/#

I ran an online chill hour calculator on your zip and it came back with approximately 850 chill hours.

There are at least 4 different ways to determine chill hours and unless you record the temperatures hourly at your residence, you are going to have to rely on a nearby reporting station. Here's the site I used: http://getchill.net/ You will need to determine your reporting station...just read the directions and it should all fall into place.

Depending on what zone map you check, you are either in zone 8b or 9. All that reflects is average minimum winter temperatures, indicating any plants with a zone 9 designation or lower will be winter hardy for you. It really has nothing to do with how well fruit trees will perform as that depends on both chill hours and heat units.

Different varieties of fruit trees are suitable to different locations/regions of the country based on the chill hours and heat units they require for good production. Your local extension service should be able to recommend suitable varieties for your specific locale.

However, if periodic flooding as depicted in the photos is a routine occurrence, choice of suitable fruit trees is a bit moot.........I can't think of any that will tolerate that situation for any longer than a day or so at a time at most. And not recurring events either.

I have updated my YouTube video to get more help.
My latest discovery is that I need to water the apple trees with 25 gallons of water each!!???!!

I have never watered the trees at all.... So is there an easy way to devise a system to water the trees??

Right now I'm thinking of buying 15 - 5 gallon buckets with two nail holes in the lower side. Then fill the buckets up every Friday. The holes of the buckets will be directed towards the tree itself, and the hole will be covered by mulch. Any issues seen with this?

Well, going from not watering at all to 25 gal per young tree is like going from one extreme to the other.

you should seriously consider planting fruit trees on berms like Fruitnut suggested. In fact, I would consider planting them in pots. This way, you can save them to high ground whenever flood occurs. Fruitnut is also an expert on planting fruit trees in pots.

like others have said, when you get that many floods a year, it will be tough for fruit trees to survive and thrive.