Doan's nursery in Belt line road in Irving has many cocktail fruit trees. I would suggest to check this nursery for fruit trees, flowering plants and tropical plants. Be prepared to wait to get help and also make sure that you are getting the right plants because many of the plants don't have labels/pricing. I also noticed that many fruit trees are from California growers, so not sure how they would grow in DFW. Moreover, they do not give any kind of warranty to the trees.

I agree with Pepino. Sounds like it could be borers. Poking is the most effective way of getting rid of them. Next winter, take a few dozen cuttings and see if you can get them to strike. If you are successful, the new trees should produce the same delicious fruit and the old one can eventually be chooped down. It would be a shame to lose such a wonderful tree.

I'd say it's Syzygium aqueum, common names include water guava, watery rose apple, water cherry, etc. Many varieties though, won't be too sure until it's fruiting.

Two books that give good information for Texas peaches are Texas Peach Tree Handbook by Jim Kamas and Growing Fruits and Nuts in the South by William Adams and Thomas Leroy. The pin holes in the leaves are caused by Bacterial Spot. It is controlled in the dormant season by using Copper hydroxide. I use it with dormant oil (oil to kill scale) in late winter before bud break. Too late to use it this year. The copper will kill the leaves. Another main problem you will have is Brown Rot (use captan or Monterey Fungi-fighter. The Monterey seems to work better. Apply before a rain and use according to label until harvest. I try to stop using it 2 to 4 weeks before harvest. Also, remove any mummified fruit and remove from property. The mummified fruit will spread the fungi to other fruit. Worms are another problem. Look up Plum Curculio. They make a distinctive mark ( a slit with a small spot). If you see this on a piece of fruit remove it immediately and spray with a pesticide. I use triazicide. You also have bacteria canker and borers to worry about. You manage canker by not pruning after June and doing most of the pruning just before or at bud break. The borers are control by spraying in the window that they appear, for me in Beaumont it is in late June. I have not sprayed for borers but will if I ever have a problem. Agrilife Extension in your county will have good information. Thinning advice, remove any twins and fruit that is oozing. Thin to about 4 to 6 inch spacing. Remember that the branch must support the full size fruit. If you have a chose between a peach on the end or one a couple of inch closer to the middle I would thin the one on the end. The fruit on the outside will usually be better quality that ones on the inside. Try to open up the middle of the trees so the leaves and fruit will dry quicker. It is easier than it sounds and some people ignore all of the above advice and still produce fruit. I can grow peaches in SE Texas and it is much tougher to grow them here than where you are.