thedarkness - maximum possible speed of growth is not necessarily what you want when you sow seeds. Google 'etiolation' for what is happening to your seedling. Seedlings are best grown at their natural pace, not forced, if you want a sturdy baby to plant out later. Apples are fruit of temperate climates. They are not tropicals. They have evolved to grow in places with definite seasons, including a cold winter. Growing them in a moist warm place is not going to encourage them to be healthy in the long run. And have you planned how you are going to get it out of the bottle later? Things would be easier if you just invested in, or found, a couple of proper flowerpots, or at least used a container with outward sloping sides. Both your soup can and the bottle will make life difficult at the transplant stage.

Some kind of white birch, which are beautiful trees but they have lots of problems. Even in the best conditions they're short-lived compared to many other species. Where are you located? That looks like a pretty warm, dry environment for white birch, which like cool, moist soil. White birches are almost always killed off by the bronze birch borer (insects) after a few years, too. I think the top is completely dead and it will spread down through thre whole tree in a season or two. I recommend that you just remove the whole thing now and replace it with something better suited to your area. Sorry, I wish I could share better news.

Shudavies, not all growth is herbaceous. tps put up shoots also from below the surface. Some people even plant tps at an angle so they will form new plants. This is called layering. This year if you haven't already cut them off wait until the leaves unroll. Then check to see if are from herbaceous or tree. On another site someone mentioned that tps are generally not shiny and herbaceous are very shiny. There are exceptions to this as for everything. If you want a tree form remove the growth if it is from the mother plant. If you want a larger shrub like plant let them grow. Each appeals it is a matter of personal likes.

Yes, just above the highest sprout is where you should cut. Use a bypass cutter about 1/4" above that last node where the highest sprout is. It's easier to cut about half the dead top initially, then the final cut will be a shorter piece that won't be as likely to tumble or fall, possibly damaging the new shoots. The tree will continue from there and down the road won't be noticeable as the tree will encapsulate that area. Those 4-5 new sprouts will all most likely try to become the new leader so you'll have a multi-leader tree if left to itself. But not to panic. Once the tree gets going you can subordinate prune all but the highest sprout on the totem pole so that high one will become the main leader. Structure pruning is a multi year project so be patient. For now, cut the dead off and let the tree grow for a couple years. And don't fertilize late in the season and cut back on watering. Trees that fail to go dormant in the fall and not harden off are prime candidates for winter kill on the new growth from the previous year. That black spot on the bark could have been caused by sun scald that is common with maples when in late winter the sun warms a section of bark then temperatures drop quickly again and freeze that part of the vascular system of the tree. But all this can be exasperated by the tree not hardening off because it's trying to grow too late in the season.