If I'm at a bar and I want, for example, drink my cup of coffee at a table outside, is
can I take it outside?
a good way to say that? Also, does
can I take it out?
have the same meaning?
Your two sentences may have two different meanings
Can I take it outside?
is the literal meaning of carrying something outside, it implies you already have your cup of coffee in hand.
Can I have it outside?
would be said if you are asking about where you can be served.
Can I take it out?
might be understood to ask if you can take it with you as a "take-out" (AmE), "to-go" (AmE) or "take-away" (BrE), which may mean you are asking for a paper cup for your coffee to take somewhere. A better formulation might be
Can I have this to go?
"Out" is used in general to mean a distance away
Let's go out tonight.
"outside" means out in the open air but possibly in a nearby area
Let's go outside on the terrace.