Answer to original questions:
1. If an amaranth species is monoecious (both male and female flowers on the same plant) as well as self-fertile, then it will be impractical to emasculate the flowers on each plant. You could try using the cytoplasmic male sterility (CMS) trait to control pollination, but this same trait could also reduce potential grain yields. One trick Joseph Lofthouse uses to encourage cross-pollination among self-fertile plants is to plant two or varieties of the same species as close to each other as possible to encourage cross pollination. There will still be a high rate of self-pollination, but the likelihood of a cross-pollination will still be higher than if the two varieties were grown in separate beds or isolated rows.
2. I have noticed similarly inconsistent germination of amaranth seeds when I attempt to sow them in unimproved soil. Many wild species of amaranth are originally native to disturbed river floodplains so they are adapted to the rich soil of riverbanks and agricultural fields. Because amaranth is said to accumulate nitrates in its leaves (according to PFAF), it would not be a good idea to use extra nitrogen fertilizer on amaranth plants.
3. From my experience, I get the highest grain yields by mass and the largest seeds from amaranth cultivars from the species, Amaranthus hypochondriacus. In 2019, I got an estimated yield of 3,607 lbs of seed based on my harvest of 5.3 ounces of seed from 16 plants. I am currently trying to see if I can select wild redroot amaranth (Amaranthus retroflexus) for improved seed production since this plant is such a common weed in my growing region, but I got poor seed yields when I tried to grow it in 2019 at only 2.3 ounces of seed from 32 plants giving only 895 lbs of seed per acre.