Bom Dia!
I) On spite - this means solely out of anger, with passion, and a strong desire for revenge! More frequently, you will see it said "out of spite" such as, "He ate his sister's whole birthday cake out of spite". This means I at her cake in anger and revenge. The reason why (what she did to upset him) would be mentioned previously.
II) This means "easy profit" as well as "take advantage". It has a negative connotation "I'm tired of seeing facebook advertisements of companies selling coronavirus cures, trying to make a quick buck off of the panic and lack of education around the virus!"
III) The original sentence you wrote is correct!! You would use might or may if you were in a formal situation, and asking permission. In this situation, you are not asking permission, and are asking a question in an informal manner. The difference between might and may is that "might I" is British 90% of the time, and "may I" is American 90% of the time. When Americans use the word "might", they use it in a very different context, where it means "perhaps" as in "I might go to the market tomorrow" - there is a chance I will go to the market tomorrow. Here is how you would use "might I "/ "may I" in a sentence. Again, note that in this case they are interchangable. "May I go to the bathroom?" / "Might I get a drink of water?" Essentially, "might I/may I" is a more sophisticated and fancy way of saying "Can I please....?".
Hopefully you found this helpful - these are very advanced questions.