I'm thinking about using a battery pack of 6 AA (12V)
An AA-battery is usually 1.5V, so 6 AA-batteries connected in serial would be 9V and not 12V. Furthermore, depending on the specific AA-batteries, they might not be able to deliver the 4A that your screen requires and the current that the rest of your system requires.
My lcd screen requires 12v and 4A
Just make sure that the LCD display really requires 4A. It seems unlikely to require so much current. Consider using an LCD which requires less current if it is the case.
I would suggest using a Lithium Ion (LiPo) battery. They are commonly available at hobby shops and on-line. Usually, they can output high amounts of current. Be sure to design some protection into your circuit against over-voltage, over-current, accidental short circuits, polarity protection etc.
is it possible to charge them
LiPo battery chargers are commonly available.
From what I understand so far, i need to wire the battery to a regulator
You are correct that you can use a voltage regulator to step down the 12V voltage to 5V for your Raspberry Pi. However, a linear voltage regulator like the one you suggest in your question dissipates power and will become hot over an extended period of time. The difference between the 12V and the 5V output voltage for the voltage regulator is also a relatively large voltage drop which will cause the heat generated by the voltage regulator to increase. Consider putting a heat sink on your voltage regulator.
A better option would be to use a buck converter for the Rpi, or even better get a battery with a higher voltage (14.8V, 4S LiPo Battery) and use two buck converters - one for the Rpi and one for the LCD. A buck converter is more efficient than a linear voltage regulator.
Edit:
As someone in the comments mentioned, rather find an off-the-shelf solution in terms of protections circuitry. There can be a fire hazard with LiPo batteries if you don't know what you're doing.
That BMS looks identical to one that I've used and it does NOT do balancing or proper charging. Just protecting from over current, over voltage and under voltage - all of which are very important.
You will need to add balance wires and get a balance charger for this battery.
Balance wires are easy - they go exactly where the bms wires go - one to each pos and neg of each cell. The balance charger will have a slot for those wires.
I recommend looking at the IMAX b6 charger because it is the cheapest balance charger I have seen and seems to work reasonably well up to batteries with 6s or less.
Best Answer
This will work for you:
CHG is the battery charger, BAT is the 12V battery, LOAD is the amp, and K1 is a Double-Pole Double-Throw relay, with K1A being one set of contacts and K1B being the other.
"NC" refers to the normally closed fixed contacts, "NO" to the normally open fixed contacts, and "C" to the movable common contacts.
In operation, what happens is that the common contact (the slanty line) is spring-loaded and, when there's no power to the coil, the spring's tension forces the common contact up against the normally closed contact, creating an electrical connection between them. When power is applied to the coil, however, the magnetic field generated by the coil attracts the common contact away from the normally closed contact, breaking that connection and forcing the common contact up against the normally-open contact, which creates an electrical connection between the normally-open and the common contacts.
The action is similar to that of a double-pole double-throw toggle switch except that the switching is done electrically instead of manually.
With the 18V supply disconnected from the circuit, the relay will be de-energized and the connection between the charger and the battery will be broken, but the connection between the battery and the load (the amp) will be made through K1B-NC and C, allowing the amp to run off the battery.
With the 18V supply connected to the circuit, the relay will be energized and the battery will be disconnected from the load and connected to the charger through K1A-NO and C, allowing the battery to be charged.
In addition, the load will now be disconnected from the battery and connected to the 18V supply through K1B-C and NO, allowing the amp to be run from the 18V supply while the battery is charging.