The number one rule of thumb that will generally answer the "is it taxable" question for any money you may have or receive: "Did you pay taxes on it already?".
Pretty much any money you actually get in your paycheck/DD has already been taxed (or at least the projected amount of tax has been withheld) is your money, to dispense with as you will (or according to your pre-arranged obligations, for most of it). Deposits paid are one such example; if you wrote a check or obtained a money order that they then cashed, that's still your money until it isn't; the contract states that it is being held effectively in escrow (though the landlord has free use of it so long as he can pony up according to the contract). Anything not used to pay for damages is yours, and you get it back.
The ATM fee refund is trickier, but basically this is a benefit offered to you as a service by your bank. You front for the ATM fees incurred when withdrawing, and then those fees are refunded to you by your bank (effectively increasing the number of ATMs you can withdraw from "for free"). As long as there is no net income, it's treated like a mail-in rebate; you didn't gain any money, so there's nothing new to tax.
There are a couple of specific exceptions to this otherwise overarching rule of thumb. One is Roth IRAs. Typically, on investments, you either pay income tax on the money going in and capital gains tax on the money coming out, or you pay nothing going in and income tax coming out. With a Roth, however, you pay income tax going in and nothing coming out, even though you're (eventually) getting back more than you put in.
Another is gifts. Whoever gave you the gift paid the taxes on it (or the money to buy it). However, if they give you a gift valued more than a certain limit (changes every year, and there's a lifetime limit), they have to pay an additional gift tax of 35% on any amount over the limit. That's taxing taxed income (usually).
There are other examples, but for the overwhelming majority of situations, if it's money you already had after any and all applicable taxes, it's not taxable even if you haven't seen that money for a while.