Hello, mona
The real grammarians out there must be busy trying to think of more rules to make our lives miserable. ~laughs~
I don't think I can help you with all of it, but I'll do what I can. and I hope I've understood your question, to begin with.
1. The four prepositions can take a noun phrase as object.
"John is as intelligent as her sister."
"I thank you for your help."
"This table is made of the finest wood."
"I'm going camping with a few of my friends."
2. I'm not sure what you mean by 'PP'. That usually means 'prepositional phrase', but I don't think it would make sense here: a preposition followed by a prepositional phrase? Can you please explain to me what you meant by 'PP'?
3. Gerunds can follow these prepositions, but I don't think that present participles can. Although both have the same spelling, they are different types of words and function differently.
"Thank you for writing back."
"I'm tired of working on Saturdays."
"What's the problem with staying up late?"
"Writing your autobiography would be the same as writing a soap opera."
4. I'll have to think about 'whether'. My first idea was to say that you can't use it after those prepositions, but the truth is that I'm not sure at the moment.
5. If I got 'tensed declarative clause' right, then the four prepositions can take one as object.
"That's the woman for whose brother I fall."
"I'm going out tonight regardless of what he may say about it."
"He's the type of man with whom I'd never go out even for a coffee."
"This isn't the same as what you said yesterday."
Let's hope all the above are correct!
Miriam