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Are the seedlings falling over because the base of the stem is weak and mushy? If so, this is called damping off, a problem caused by fungus that frequently strikes young, seemingly healthy seedlings. You can read more about it here:
https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/what-is-damping-off.htm

Are your seedlings growing in the right conditions? It's possible they're using up all their energy just to germinate, then failing because there's not enough of something to sustain them. Indoor tomato seedlings need warm, moist soil and plenty of bright direct light. You can read more about their requirements here:
https://www.gardeningknowhow.com/edible/vegetables/tomato/growing-tomatoes-from-seed.htm

Yes, as long as the plant is an indeterminate variety, I think it will continue growing after being cut back and produce fruit. I am not sure whether they would grow from new canes or old canes, and I don't know the details of perennial tomato pruning, but maybe you could contact a local extension agent for advice.

These links will help you with this pest issue.

https://www.gardeningknowhow.com/plant-problems/pests/insects/getting-rid-of-psyllids.htm
http://extension.colostate.edu/topic-areas/insects/potato-or-tomato-psyllids-5-540/
http://extensionpublications.unl.edu/assets/pdf/g2113.pdf

Yes, we have heard of these uses in the garden.

We do recommend composting your Banana peels. The link below has more information.
https://www.gardeningknowhow.com/composting/ingredients/banana-peels-compost.htm

Epsom Salt is a great product for the garden. I myself use it regularly in my herb and vegetable beds.
Here is a link that has information on using this inexpensive product.

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/epsom-salt-gardening.htm
https://www.gardeningknowhow.com/lawn-care/lgen/using-epsom-salt-on-grass.htm
Now if you friend is having success with a certain technique, by all means give it a try! That's how we all learn!

Certainly, yes they can grow and produce.
If your plants were Hybrids, they may not resemble the original variety.
If you were growing an heirloom variety, they will be true to the parent plant.

Upper leaves that appear knotted could be a symptom of a viral disease, a nutrient deficiency, or herbicide exposure. Please see the links on this page to tomato bunchy top and tomato apical stunt viruses and herbicide exposure symptoms:

http://vegetablemdonline.ppath.cornell.edu/DiagnosticKeys/TomWlt/TomWiltKey.html

It looks like "Good Natured Knock Out Nematode" is actually a live beneficial nematode product. It definitely wouldn't have caused these symptoms, and it should help get rid of any root knot nematodes (if you had them) and certain other pest problems.