If I would like to make requests, should I use “I was wondering…” instead of “I am wondering…” and “I wonder…”? If yes, what’s the most appropriate situation to use “I am wondering…” and “I wonder…”?
While technically the three phrases differ in tense, they all have the same meaning. I'd suspect that "I was wondering" is used most often, followed by "I wonder". "I am wondering" would probably be reserved for cases where you're really perplexed because it suggests the wonder continued over a longer period of time.
"I was wondering" can be used to make indirect polite requests. For example: "I was wondering if I could borrow your book." "I was wondering if you could drive me to the airport."
"I wonder" is not used for indirect requests. It is usually used to express your thoughts, such as "I wonder if he would let me borrow his book." "I wonder what happened."
"I'm wondering" is used like "I wonder" but denotes the present progressive, such as "I'm wondering what to do next."