"Is there a map?"
To quote (https://www.learn-japanese-adventure.com/arimasu-imasu-existence.html), use は with あります/います when both the speaker and listener know about the SPECIFIC thing, you are asking where the specific thing is, or with negative answers/statements.
In this case, it is a question about a map specific to this area you are in (which we mean when we ask "Is there a map?"), not some random map that won't be any use to you. Think of it as "The map, is it there?" or "The map, do you have it?".
I think this is a very good explanation: http://nihonshock.com/2010/02/particles-the-difference-between-wa-and-ga/ . But it took me a bit of studying until I actually felt like I understood it. Also, some of the uses are idiomatic and hard or impossible to guess a priori.
This is great. Also, some idiomatic uses become more clear when you understand the underlying grammar. For example, "x ga suki desu" is hard until you understand that suki is an adjective in japanese "x is likeable (to me)" so you use ga because there is always an invisible "watashi wa" before it.
Not necessarily. Ga makes the question more 'is there a map' rather than wa, which mahes it closer to 'could I see the map.' Languages seldom translate neatly. There are always loads of exceptions to perceived 'rules,' and one needs to remember to be flexible in learning.