You shouldn't need to remove the potting soil unless it is really contaminated with salts or something. You should be able to transplant soil and all. Depending on exactly what plants you are transplanting, you might want to break up the edges a little so that the roots will grow out into their new soil better. Of course, don't do that if you're dealing with a plant that doesn't like it's roots disturbed.
It's fine to fertilize first year plants, providing that they actually need the fertilizer you're applying - just like any age of plant. Get your soil tested and/or pay attention for symptoms of nutrient deficiency.
I remove as much as the potting soil as possible without causing the plant too much stress and dont spend gobs of time doin it either. This can be a gentle shake or something a bit harder.
You want the roots to move out of the planting hole and into the surrounding soil. Having a hole with radically different soil (and potting soil is radically different) usually impeeds root developemnt and spread, and can cause drainage problems. Just knock off as much soil as possible and incorportate it into the planting hole (or not) and plant away.
If your plants are already potbound and you end up having to cut or really break the rootball you won't be able to knock off any soil and are starting at a deficit already as far as healthy plants go.
I water/fertilize with very weak manure tea for all plants.