Can I patent something like this?

A patent within a patent... patception

If the things that you put together to make your thing are already patented you might have some difficulties. Most people patent their own inventions, not things they put together with other normal objects. You can try, though.

Yes. The issue with patents is that it cost usually more than it may be worth. If it's an original idea, but short lived, then it may not be feasibly. The hola hoop toy was patented, but it doesn't stop anyone from selling a hoop, if any one stills wants one. It's more a business because getting a patent for a hoop for example could be more than the invention

Yes, a huge number of patents are made from "non-obvious combinations" of existing inventions. Merely "putting a clock" onto something would probably not modify its function or structure in any patentable way, so that would not qualify as an "improvement patent". But if you think of a new way to put several ordinary things together to improve the function or other characteristics in a useful and non-obvious way, you should certainly consider discussing it with a licensed patent attorney before you accidentally lose your rights to file for a patent (e.g., by disclosing it in public).