When raising sweet peas from seed, should the young plants be pinched, and if so, by how much and at what height?
Yes, pinching makes for a fuller plant. When the seedlings have 3-4 sets of "true" leaves, just nip off the very end of the plant, just a centimeter or two is all you need to take off.
They die back each year but don't return.
It sounds as if you may be growing the annual sweet pea variety rather than the perennial, which returns each year. Make sure you are growing the right one. If you are growing the perennial variety (Lathyrus latifolius), they will reseed themselves each year. Lathyrus odoratus is the annual type.
How does changing the type of water affect the growth of a sweet pea plant?
Different waters have different minerals and nutrients.
Can you tell me what bush cucumbers are? Can sweet peas be grown in an upside down garden?
Bush cucumbers are cucumbers in which the vines grow in a more compact shape.
You can try to grow sweet peas upside down, but they will most likely climb back up the side of the container as they like to hold onto things and climb upward.
How and when can you transplant a perennial sweet pea? I live in Zone 3-4.
In your area, it would probably be better to wait until spring for transplanting. Try to keep the root ball together. Plant it at the same depth it was originally growing. Lightly firm the soil around it and water. Wait 7-10 days and then add some mulch but be sure to keep the mulch at least an inch away from the stem of the plant. It may also be helpful to trim off any blooms that may be present to reduce shock while the plant establishes itself.
I have Sweet Pea Vines growing over an ant hill. Will the vines thrive there or would some other vine be better?
They should be fine. Ants normally only bother plants if the plants get infested with aphids (the ants feed off aphid secretions). So, they should not bother your sweet peas as long as they are healthy.
How do I get rid of hard, black insects in sweet peas?
Try neem oil. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm