When should I advance my rook pawns ?


it's quite a deep question. The demands of the position of course overrule any generalisations but here are a tentative few:
Attacking:
1/ When you castle opposite sides and start or continue an attack with the rook pawn (or knight pawn) on the other flank. The rook's pawn often comes into the equation against a fianchetto position where it is used as "lever" to open a file. By the same token if the defending side has played his rook's pawn forward a square then the knight's pawn advance is often a good option to attack that as well as a typical knight on the bishop's three square. (These pawn moves in front of the king can be aggressive of weakening depending on other considerations viz centre etc and this where generalising has to give way to analysing).
2/ When castled on the same side but the centre is closed.
3/ On the same side when you have a central preponderance that can't be challenged.
Defending:
4/ To break a pin on your knight - BUT be aware of a sacrifice of a piece taking your rook's pawn
5/ Creating a bolt hole for your king if there are back rank threats.

The post number 2 is the answer. Modern Chess is based on in depth analysis of the position, not principles.

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