You are right! you can also say 老大爷，大爷，老爷爷，爷爷，老先生，老爷子。you will be more polite

This also depends on whom you are talking to. If you are talking to the old man, if you say 老头儿, it will be very unpleasant, you'd better use the suggestions above. If you are telling other people something like there is a group of 老头儿 are playing chess in park, I think it's quite ok. Anyway it's a very informal expression, and you won't find it in any formal document.

Hi, 老 is a adj, 头 is a noun, but the 儿 is a Rhotic accent. The 儿 mean nothing, but it change the pronunciation of 头。 In writing, we write 老头，then we pronounce 老头儿. It's kind like want to and wanna.

你也是会说”老男”

Yeah. 老 is an adj. 老头儿 is a n. However. You have to know. The latter one is quite rude. I believe most of old man don't want to you call them in this word. If you want to performance more polite. You can call them "老人家，老先生，爷爷，大爷“etc.