In Spain, (Seville anyway) when you want a second beer and ask for "a beer" (una cerveza,) the barkeep will consistently refer to it as "otra cerveza" ("another beer.") That's not an implication about your drinking. It is normal** to ask for "another beer" after the first one. Otherwise, it apparently doesn't sound right.
* "Are y'alright" can also be a way of confronting you, if you're acting the bollocks or doing something that the speaker thinks you shouldn't. Again, it means roughly "may I help you" the tone of voice expressing one's implication.
Some barkeeps will calculate the "tab" in chalkmarks atop the counter in front of you. Some will keep the record on paper, and some will remember. Some will just ask you how many beers you had, when you're ready to pay and leave.
Return to "normal to ask for 'another beer'" ...