I share your passion for limes... and here are my experiences re your questions:
unfortunately, they are not everywhere, at least not all the time. In such places as VAnuatu
they are seasonal and imported ones are not available once away from pt Vila. I suspect that this is true in many third world cruising grounds.
They range from nearly free to bloody expensive! Here in Oz, we see prices of ~30 AUD/kg regularly (that's a couple of bucks each). In season, they drop to ~5 AUD/kg, which is bad enough!
When they are cheap
, we buy them by the dozen, and wrap them in Aluminium foil. They last for a few weeks like that, depending on their age when picked and when actually sold. When they are at their price
peak, we tend to grimace and walk on by.
We spend most of our time in tropical or near tropical areas when away from civilization, and there they are usually available in season. I suspect there are indeed places where they are never available.
The best kinds? I dunno! The little "limones nacional" sold in Baja
are pretty damn good, and always inexpensive. Don't see that sort out here, and what are sold here are usually labeled "Tahitian limes", whatever that means. They are quite flavourful too...
What is really good to find are locations where both limes and good rum