In continuing to add ammonia when there's a small amount of ammonia already there (0.50), am I risking this cycle going on forever in the form of a high nitrite as the nitrite-eating bacteria keep struggling to keep up with the ammonia-eating ones?
Nope. Normally people go with around 3-5 ppm ammonia so I don't see an issue adding a bit more than what you have. The nitrite-to-nitrate bacteria should be able to keep up since you're showing nitrates.
This may be idiotic - bear with me: Since I already have nitrate present (around 40 now), and this tank is NOT going to be heavily stocked, is there a chance that the reason I'm showing such high nitrites and even still showing ammonia because there's SOOO much gunk in the tank (flake food and a ton of snail poop), and if I was to clean that stuff up, those levels would fall to 0 and I would indeed have a cycled tank? In other words, is it possible that it IS cycled now but badly out of whack because of all the gunk? Or is that wishful (and dangerous) thinking?
Hard to say. I'd let the the ammonia get converted completely and let the nitrates rise a bit more than that...to be on the safe side.
Also, once I'm finally cycled (0 ammonia, 0 nitrite, measurable nitrate), and I do a 50+% water change and gravel vac, do I also squeeze out the foam that's at the first level of the filter (have Eheim substrat as second & third levels)? The foam has to be FULL of the gunk I've been throwing in that tank... ? Obviously I know not to CHANGE the foam, but do I swish it out in used tank water once the cycle is over or leave it be?
Shouldn't be an issue.