Yes, you can plant now but you will need to monitor watering very carefully for the rest of the season.

I would ignore those instructions from the nursery :-) They are out of date and inaccurate. With clay soils, you want a very wide by quite shallow planting hole and to site the rootball high: "Dig a shallow bowl-shaped hole slightly more shallow than the height of the rootball (from the bottom of the rootball to the root flare). The root flare of your tree or shrub should lie just above the surrounding grade after planting is complete. Don't leave loose soil in the bottom of the planting hole. If the hole is accidentally dug too deep, fill the bottom of the hole and use your foot to firm the soil before moving the plant into the hole. Leaving loose soil below the rootball can negatively impact drainage and lead to rootball settling. The diameter of the top of the planting hole should be at least twice the diameter of the rootball. Wider holes are even better, especially in harder more compact soil. If planting a bare root tree or shrub, a cone of soil can be left at the bottom of the planting hole on which to place the root system. When planting in clay or wet soils, roughen the edges of the planting hole with the tip or edge of your spade to reduce the interface/boundary often formed by compacted/glazed soil resulting from the digging tools pressing against the sides of the hole."

Personally, I would remove the fiber pot but not until the tree was sited correctly in the planting hole. It will break down eventually but IME, not nearly fast enough to accommodate good root growth. If you are concerned about removal, do cut off the top portion of the pot so that none of it is showing above soil level. And be sure to slash the sides to allow the roots to spread easier (and the pot to rot faster).

The banana and egg stuff is also old wives' tales material :-) Just plant the tree in the hole as described above, backfill with whatever soil was removed and water in well. It won't need any fertilizer until next spring, if it needs any at all.

And you can attempt to straighten the tree just by a slightly angled placement in the planting hole but not really necessary.....the tree will straighten itself as it grows.