How do you handle character thoughts?
1. She looked at him suspiciously.
2. She looked at him suspiciously. Yes, sure. The guy thought she was stupid.
3. She looked at him suspiciously.
Does he really think I'm going to believe that?, she thought.
This guy thinks I'm stupid.
4. She looked at him suspiciously. Yes, sure. I mean, what can I tell you, dear? That guy thought she was stupid, so clearly he wasn't understanding anything.
And so on.
Should they also be in third person, past tense?
In this case the narrator acts through the telling, therefore it is not necessary to use italics because he is the one who is saying what the character thought at the time. It is similar to example 2 and 4, although the latter is an invasive narrator and also occupies more pages, a girl in a bar who talks up to her elbows telling the story to a friend. What she tells is in the past but the analysis, her comments, are obviously in the present tense.
BTW, what kind of story are you working on,
@Wayne Mack? Because if it is a mystery it is more atmospheric and perceptive, therefore one focuses on the environment, which is sinister even if it seems like a day at the beach, and on the reaction of the characters. Primary, in most cases because if something scares me I'm going to jump even with the crack of a branch. I am not gonna to think much; the "a lot" is what is happening around or what I know is a lot but I can't know what it is. Ay, mom, get me out of here!
It is different, for example, if you are writing a historical novel, something Napoleon type, in which the thoughts of the types are adapted to the ideas they had about those historical events and even later reflections. Danger of accusations for info-dumping: 50%. Bah.
On the other hand, in another Kafka-type novel, the entire novel is a succession of thoughts, it is a psychological novel. DAID: 100%.
A variant of that is Michel Houellebecq, where it is possible to find some dialogue and eventually something happens. DAID: 75%.