Catch up with or catch up?

I have taught English to my country people. I am not a native speaker, even though I put in my two cents for those who post questions here. There is one thing that has bothered me. I would appreciate your help. Please take a look at the following sentence.

"He was too fast. I couldn't catch up with him." This statement sounds correct. But when these two sentences are combined into one, should it be "He was too fast to catch up with."
or "He was too fast to catch up."? Grammatically, the first one is correct, but the second sounds ok to my ears. Do I have to see an ear doctor?

Similarly, which one would be better?
"I have a lot of work to catch up on."
or
"I have a lot of work to catch up."

Here's a similar one.

I need ten dollars (pounds).

1) Is that too much to ask?
2) Is that too much to ask for?

Similarly,

I'm so glad we chose this hotel. It's perfect!

3) What more could a person ask?
4) What more could a person ask for?

I frequently hear it without "for", and it sounds strange to me, and yet even stranger is "For what more could a person ask?"

Comments?

No, I don't think so at all. That "rule" about not ending a sentence with a preposition is pretty much a bogus rule. The best writers do it all the time.

The original sentence, if "sanitized" as you recommend, would, paradoxically, end up even more awkward:

"He is too fast up with whom to catch." :(