Help!

[English Maiden]

Hello again, sir!
Could you please explain to me why we say "I was wondering if..." and not "I am wondering if..." when asking for a favor or verifying something. And suppose I'm in class and a classmate approaches me and asks if I am prepared for our exam in one of our subjects, but I forgot about it. Should I say "I forgot we HAD an exam today" or "I forgot we HAVE an exam today"? I go with the latter since the condition of having an exam still exists. Could you also help me identify which one in each set of sentences is the correct one?
 
I realized I liked you.
I realized I like you.

She said she was pregnant.
She said she is pregnant.

I didn't know your name was Mary.
I didn't know your name is Mary.

I told her that I was leaving for the US in June.
I told her that I am leaving for the US in June.

Thanks!

[Joe Carillo]

Prefacing a request with the expression “I was wondering if...”, as in “I was wondering if you could lend me your tire gauge,” is a polite and deferential way to ask for a favor from somebody—more polite and deferential than just saying “Please lend me your tire gauge” and much less demanding than “Could you lend me your tire gauge?”

In contrast, when someone prefaces a statement with “I am wondering if…”, as in “I am wondering if that guy will lend me his tire gauge,” it’s normally when talking aloud to himself or herself—whether alone or in the presence of another person. It’s a way of sizing up the possibility of a particular request being granted before that request is actually made to the person concerned. It’s flat-out wrong and improper to address a request prefaced by “I am wondering if…” directly to the person requested; for that purpose, the past-tense preface “I was wondering if...” should be used.

For the second situation you presented—when a classmate approaches you and asks you if you are prepared for the exam in your class—you have correctly chosen “I forgot we HAVE an exam today” instead “I forgot we HAD an exam today.” This is because, as you have correctly surmised, the exam has not yet taken place; if the exam has already taken place, however, the latter version would apply: “I forgot we HAD an exam today.”

For the sentence pairs you presented, the sentences set in red text below are the correct usage:

“I realized I liked you.” (Improper form that should be avoided. It can be perceived by the person addressed as an insult.)
“I realized I like you.” (Correct as a declaration being said now.)

“She said she was pregnant.” (Correct as reported speech for something declared in the past.)
“She said she is pregnant.” (Correct as reported speech for something being said now.)

“I didn’t know your name was Mary.” (Correct as declaration of a supposition made in the past.)
“I didn’t know your name is Mary.” (Correct as a declaration of a supposition being made now.)

“I told her that I was leaving for the US in June.” (Correct as a declaration of something said sometime in the past, and it’s already past June.)
“I told her that I am leaving for the US in June.” (Correct as a declaration of something said sometime in the past, and it’s not yet past June.)

[English Maiden]

Thanks a ton for your answers. They are really helpful! (Or should I instead say "They were really helpful" since I already read them?) Another situation I often have trouble with is when something that someone says to me offends me, I don't exactly know which tense my verbs should be in in my response. Suppose the insulting remark has already been said to me, should I reply "I WAS offended by what you said" or "I AM offended by what you said"? I'm guessing the correct response is the former, but I can't be sure and won't be able to stick to it at all times. The latter response seems okay to me in that by the time I say that response I should still be feeling offended. Gah, I am really confused! This may seem laughable to many since it's very basic English, but I am really unsure. I'm hoping you can still help me with this. Thanks again!

[Joe Carillo]

Since the offense still subsists at the time of your speaking, the correct response should be in the present tense: "I am offended by what you said." When referring to a feeling or state of mind of yours in the past, use the past tense for that response: "I was offended by what you said."

[English Maiden]

Thank you again and again, sir, for your immediate answers. Really, I can't thank you enough. In no way do I want to be abusive or perceived as taking advantage, but could you still provide answer to the  following question? If, for example, I made a promise to a female friend today to take her to the beach at an indefinite time in the future and I intend to keep that promise, how do I share that information with another person? Should I say "I promised her that I'll take her to the beach" or "I promised her that I'd take her to the beach"? I'll be waiting for your reply. Thanks!

[English Maiden]

And I have yet another thing I'd like to ask you, sir. Ha ha! How would you rate my English proficiency? Am I on (or at?) that level where I can start writing professionally? I'd appreciate if you'd be completely honest with me. I'd really like to improve my English, so I can speak and write better in it. Would you advice taking a creative writing course first? Did you take such a course too? I'm looking forward to your answers. Thanks a lot!