1. For easy access to good bars and restaurants
, I would definitely recommend the old quarter of the city, also known as the historic centre of Malaga where you will find two main tourist points that will appear on any map, which are the Picasso museum and the Plaza de la Merced (the Merced square). This whole area is packed with the best backstreet places for food and drinks: Tapas bars, Wine bars, Restaurants and Pubs for all tastes of ambience and music.
2. Generally, price wise there isn't much of a difference between "main stream" and "backstreets" but regarding quality, yes. Most of the locals in Malaga centre know where to go when it comes to bars and restaurants with the best Price/Quality relationship, so I would always recommend to hit the backstreets and stop at the place that you see most packed; you may have to wait a bit to be seated or attended but that happens to everyone and it's well worth the wait.
3. The train service from the airport to Malaga city
is the simplest task. To buy your train fare, there are several machines right on the platform that all have touch-screens in which the first page you'll see is precisely to choose your language, it will then guide you through very easy steps and will finally print out your ticket. Be aware to check the signs that you're on the right side of the platform as one side will take you towards Fuengirola and all the rest of the Costa del Sol destinations and the other will take you straight into Malaga centre. Once the train arrives and you hop on it, there's nothing else to worry about as you get off at the last stop so you can relax for 10mins til you get there.
An extra tip: Once you walk up the stairs and exit the train station
, you'll find yourself right in the city centre and if you were to take our advice and stay in the old part, unless you are carrying a lot of luggage, I wouldn't even bother catching a cab as it is only a 10 - 15 minute walk, if that. (obviously I would try to ask for directions from the station so you don't end up walking towards the opposite direction but it's fairly straight forward and easy to find)
Also, don't forget to visit the Alcazaba which you'll also find very near to where you'll be staying and contains plenty of Malaga's history and breathtaking views of the whole city and port from the top!
Hope you enjoy your stay!