No not really.....A little soft wouldn't worry me...As long as you have a healthy potato with eyes, you should have plants..

You can hill with just old garden soil, as log as it does not get hard like a rock. That is how commercial grower do it. The soil (or anything else) that you hill with does not need to have any nutrients, but it is best to be fluffy so the tubers can grow in it. The nutrients comes from the roots grown out of the seed potato.

Right, at the level of the seed piece and somewhat higher, the tuber-bearing filaments come off the stalk as long as it is kept covered with soil or mulch. Generally speaking once the stalk is quite green it will no longer make tubers from that point, which simply means the plant will put more energy into fewer tubers not necessarily less yield. I make a shallow trench to put the seed into and cover with one or two inches of soil. In the bottom of the trench first goes compost unless the ground is fairly rich. A sprinkling of epsom salt is good and wood ashes if you have any. When the plant is vigorously growing N can be supplied with urine diluted 5 or 10 to one with water. Potatoes like tomatoes are highly symbiotic with mycorhizzae. If you can find old wood chips or twigs with fungi on them toss them in the compost in the trench and soak the trench good of course. One can also buy the spores by mail and inoculate the compost or rotted manure, etc. Once the garden area is well grown out with myco you're all set if you don't till too much, keep the OM up, don't let the ground get bone-dry with means don't let it be bare for long periods. Even weeds help. Every common crop family except brassica needs the myco's for optimum health.

No, you do not "have to" hill potatoes, and planting the seed potatoes deeply is a different way of achieving the same goal. However, planting deep only works if you have well-drained soil. If someone plants too deeply in soil that is cold and holds moisture too long, there is a very real risk that the seed potatoes will rot before they sprout. I usually plant my seed potatoes 8" deep but only put a couple of inches of soil on top of the seed potatoes and leave the rest of the soil sitting beside the hole. As the plant emerges from the soil, I rake more soil into the holes and fill the holes in over time. That way I can keep an eye on the potatoes and know they are growing, rather than planting them 8" down and then wondering for a month or more if they ever are going to emerge from the soil. I think you should do whatever works for you in the conditions you have. If you get good harvests from planting deeply, why change? However, be really careful in an extra-wet year unless you have soil that drains incredibly fast. Potatoes planted that deeply in cold, perpetually wet soil struggle to survive. You know how potatoes grow, right? You plant the seed piece and stolons grow upwards and outwards and roots grow downwards. Eventually, tubers will form on the parts of the stolons that are underneath the soil. Sometimes, as the tubers (which are your potatoes) enlarge, they break through the surface of the soil and sunlight hits them. Wherever the skin of your potatoes is hit by sunlight, solanine (a poisonous substance) develops, your potato skin takes on a greenish tinge and the potatoes develop a bitter flavor. Hilling or mounding soil around the base of the plant before potatoes bust up out of the ground prevents the sunlight from reaching the potatoes and turning them green. Because I generally grow potatoes in raised beds, I plant deeply instead of hilling. Normally, you'll get potatoes forming along roughly 6-8" of underground stolon. Sometimes, though, they'll form a little higher. I don't like hilling in raised beds. First, it just looks silly. Secondly, wind and rain erosion can wash down or blow away your hills. So, I plant deeply and then, around the time that the tubers start forming, I pile on the mulch thickly. The mulch, if applied thickly and packed down, keeps sunlight from reaching the tubers and turning them green. Some people believe that you can keep hilling indefinitely and more potatoes form along the stolon. However, I don't know anyone who ever has been able to produce tubers in our climate along more than 8-10" of stolon, even if they piled on another foot of soil as a hill or a foot of mulch. Heat does impact the plants' ability to form tubers, so here in OK, no matter how deeply we plant or how high up we hill or mulch, there's only so many potatoes the plants have time to form before it gets too hot for tubers to set and size. Do what works. I've tried growing potatoes every which way and my favorite way is deep planting with mulching later in the season instead of hilling. In a really wet year, though, I'll plant more shallowly and hill because if I plant deeply, the seed potatoes rot.