When the cider is done fermenting I rack over to a carboy for a few reasons, the first being to rack off the lees/sediment, the second is to let it age and clear, more sediment will drop out of suspension, don't worry too much about it.
I've been making wine and cider for years, and never once did I have either become oxidized, or get an infection, I think that there is a little bit of infection hysteria lately, as long as you are meticulous about washing and sanitizing everything, you will be fine.
A teaspoon of nutrient per gallon is normal for certain nutrients, it really depends on which you are using, and what the directions dictate, there is a difference between beer and wine nutrients, in the future, I recommend using Fermaid K for Cider and wine.
Depending on what your SG was, you may need to age the cider for a few months, my apple wine usually bulk ages for 12-15 months, my ciders which I like to keep between 6%-8% abv will age a month or two, followed by adjusting the cider to our tastes by back sweetening, filtering and priming as I would beer, and bottling.
When the cider is carbonated, I pasteurize.
