what is the appropriate name for these women, since nobody refers to them as strippers ?
They are simply chicas! That's the most universal term. To be overtly polite you could use the term "bailarina exótica." "Stripper" also works, just say it with the spanish accent like STREE-pehd.
Funny story, beginning of the last trip I was with two chicas and referred to them as bailarinas exóticas, and one chica was like "No somos bailarinas, somos strippers." Later in the trip I was with a different chica, and called her a stripper and she corrected me back to bailarina exótica. Just stick with chica!
Avoid the term puta. It can mean bitch or whore, one of those words where if she says it its fine but you as a gringo should avoid.
Do I just walk up to someone I like and say :
I start by introducing myself, then offer a beer.
Hola, buenas noches ¿cómo estás? Soy Ron, cómo te llamas? De dónde eres?
Half the time a mesero will interrupt to ask you to buy a ficha before you even have that conversation.
¿Puedo conseguirte una ficha?
She'll understand you, but this sounds weird, to me. The ficha (chip) technically is the receipt she gets (worth like 3 USD) for selling the beer. Try:
¿Quieres algo tomar? / Want something to drink?
Very natural and mexicano, but leaves you vulnerable to the dreaded wine ficha, which you must avoid (No vino, por favor!) if you are on a budget. So instead you could say:
¿Quieres tomar una cerveza conmigo? / Want to have a beer with me?
Or can I just ask in English.
Yep, you can definitely just use English. I'd say like 70% of all chicas are proficient enough in English to introduce themselves and negotiate a transaction.
¿Cuánto por el sexo?
¿Cuánto por un arriba contigo?
Yep, she'll understand this. You could also ask it like:
Quieres ir arriba contigo. ¿Cuánto cobras?
Since I'm a gringo, what are some major social mistakes I can avoid while traveling.
Make sure you tip the little guys in Mexico. They don't expect much but do expect to be tipped. Obviously you'll remember to tip the meseros and chicas, but I'm talking like the robe guy ($1), the shuttle guy $3-5, the viajeros (hotel attendants - tips depending on what they do for you.)
Enjoy, I hope to read a good report or two!