Do all penises have some goosebumps on them, or is it some kind of problem?

Most do! Most do and some more prominent than others. Just leave them alone and don't worry about them. It is just the way we are made. This is not a beauty contest!
Yes. Ring of tiny bumps around glans corona of penis are so called "yyson's glands" & are normal, more obvious in uncircumcised males & after puberty.