The "rule," such that it is (and please note I put rule in quotes

), I've seen for using italics for internal dialog is to "only" do it when you are either using an I statement in third person narrative, or using present tense in past tense narrative.
But like any other rule, there are exceptions. I read a book a while back where the writer did not use italics for these situations (and did not tag them as thoughts), and I found it a bit jarring to find an I statement in the middle of a third person paragraph or to see a present tense statement/perception in the middle of past tense narrative. But I'm not used to seeing authors do this, probably because most of the authors I've read in recent years use the italics method.
I have also seen authors who tag every line of internal dialog (she thought), and thus bypass the italic issue. I think Jean Auel did this in her books. But the current style trending towards eliminating tags whenever feasible, may explain why italics are used a lot.
Whether or not to use italics for other purposes gets stickier, as the more things you use them for, the more potential for confusion there can be. Also, some readers find long paragraphs of italicized text to be annoying or distracting.
I read a lot of SF and fantasy, so I'm "used" to seeing things like telepathy, mindspeech and other forms of nonverbal dialog italicized (the Anne McCaffrey approach). But it works best if the individuals communicating in this manner are on the laconic side, I think.
You could also use normal quotations, but tag the dialog (or describe associated actions or perceptions) in a way to make it clear it's non spoken.
I agree with the others who said there's no "set" way to handle these things, so long as you're consistent.