Advice on Mexico

Hello all! I was hoping I might be able to get some good insight and opinions from all of you who have already made the leap! Here is my situation: I am looking at moving to either the Tulum/Playa del Carmen area of Mexico; San Carlos, Panama; or Fajardo, Puerto Rico, from the US. I will be employed as a remote employee for a US company (but will get my own residency visa). I'm in my 40s, female, and will be moving alone--aside from my 2 dogs.
I was wondering about a variety of things: how safe a woman alone might feel; how tolerant people are to Pitbulls; any tips/tricks on renting (dealing w/real estate agents/landlords); a good lawyer for the visa; good places to go to buy groceries you miss from home; how reliable is the internet connection at home; will I be lonely (lol); best way to get my belongings there; things I should definitely bring, or leave behind; what if I want to keep my US cellphone, do I just get a local SIM card; buy a used car there, or will a scooter suffice; are medical expenses all out of pocket for temporary residents; will online products (Amazon, etc.) ship there?
I realize those are a lot of questions, so don't feel like you have to answer them all, but any advice is appreciated!
Thanks so much!

Welcome Tankgirl,

Wow, this should keep us busy for awhile.
Let me start the ball rolling by answering 2 or 3 from my perspective.

I have used Amazon a number of times, yes they will ship many things to Mexico.
There are a number of stores that provide most of what you would get in the U.S.  Food depends on what you are looking for.  The stores are arranged differently than in the U.S. so you have to figure out their system. The people are very helpful, and tolerant.

Those that speak at least some Spanish make friends much more quickly. Those that do not , can have more problems. Plus there are expats in many areas, especially Playa and Tulum. Tip Tulum is hotter and more humid than Playa.

Places where you could get into trouble are the same places you might get in trouble as a single female in the U.S.

Thanks travellight, I really appreciate your insight!