Your question actually contains four questions—the third and fourth ones largely repeats of the first and second ones, respectively. I'll try to answer them in the order in which they appear.
If the text I am quoting is italicised or bold, does my quote need to include this?
If the original text that you are quoting contains certain individual words that are italicized or bold, then fidelity to the original text requires either that you reproduce them in their original italic or bold font, or that you indicate that you have done away with the author's differential, typeface-based treatment. You can accomplish the latter by adding a note in square brackets at the end of the quotation that says something like "[italics in original removed]."
I can think of two exceptions to this general rule. One involves situations where the entire quotation was originally set in italics or bold (as for example in an advertisement or in promotional material or in a caption), in which case no difference in internal emphasis results from converting the italic or boldface font to a regular roman font. Just as you are under no obligation to retain the original typeface (say, Palatino) in your rendering of the quote, you are free to drop across-the-board italics or boldface. A second exception involves quotations from very old content (from a time when proper nouns were consistently initial-capped and italicized) or from promotional material (where a product name might be bolded or all-capped, the better to make its presence brazenly known).
If I want to emphasise something in the quote, can I make words italic?
Yes, you can add emphasis to a particular portion of a quotation—but when you do so, you should indicate the fact by adding in a square-bracketed note words to the effect of "[emphasis added]."
The practical exception here is a situation in which the author has already italicized or bolded certain parts of the quotation and you want to emphasize others. It's possible in such a case to insert "[emphasis added]" notes after each of the additions you introduced and to insert "[emphasis in original]" notes after each instance of italics or bolding that the author introduced, but the effect quickly becomes quite unpleasant and I would advise you to forgo adding your own emphasis in such situations.
Can I quote that ["I love apples. I really love them!"] as "I love apples. I really love them!"?
As indicated in my answer to your first question above, you can drop the italics from really; but in a formal setting, you should note the omission.
Also, could I quote the beginning as "I love apples,"?
As noted in my answer to your second question, you can add italics to a quotation as long as you acknowledge the alteration, as in "I love apples [emphasis added]."