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For example if I m facing orange what would you do
 
You should rotate if it takes several F moves. If you do them right, they can be much faster than a y rotation(the worst rotation). For example, inserting a pair. But if you have a case such as R U' R' U' R U' R' U R U' R' but rotated, it's much smarter to do a y to turn it into a very fast RU case than doing 6 F moves. Basically, a couple F moves is faster than rotating, but a lot of them is bad, especially if a rotation makes it RU or LU
 
You should rotate if it takes several F moves. If you do them right, they can be much faster than a y rotation(the worst rotation). For example, inserting a pair. But if you have a case such as R U' R' U' R U' R' U R U' R' but rotated, it's much smarter to do a y to turn it into a very fast RU case than doing 6 F moves. Basically, a couple F moves is faster than rotating, but a lot of them is bad, especially if a rotation makes it RU or LU
I think that it is basically not fast=slow to “mirror“ (R/L into F/F‘) an F2L alg. In my opinion F can be useful for empty slot cases and for some other cases, for example: F‘ L‘ U2 L F

Btw, how is it called to turn a R into F/L into F‘/etc. ?
 
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Let’s say I inserted first two F2l pairs in back slots and two empty slots facing me. Then I got a case that I can’t insert by only doing R U L moves, would you rather do a rotation or F moves? ( i.e rotation or regrip) or are there any ways to solve this better?
Use an F move if its beneficial to your EO, you can avoid all dot cases and force cross cases easily if you use the right insert at the right time, but as a rule of thumb (for me at least), if its last slot, then use an F move, if there are other unsolved pairs, rotate.
 
Let’s say I inserted first two F2l pairs in back slots and two empty slots facing me. Then I got a case that I can’t insert by only doing R U L moves, would you rather do a rotation or F moves? ( i.e rotation or regrip) or are there any ways to solve this better?
if the next pair is a good edge, dont rotate
if the next pair is a bad edge, rotate
prevents double rotations

if its last slot, it doesnt really matter
 
Let’s say I inserted first two F2l pairs in back slots and two empty slots facing me. Then I got a case that I can’t insert by only doing R U L moves, would you rather do a rotation or F moves? ( i.e rotation or regrip) or are there any ways to solve this better?
I do F moves to take out misoriented edges so they become oriented. If an edge is misoriented in the top layer I rotate.
 
I do F moves to take out misoriented edges so they become oriented. If an edge is misoriented in the top layer I rotate.

Doing an F move or doing a y' R' is literally the same thing from two different angles, so it doesn't change EO at all. It's like doing Petrus F2L with the 2x2x3 in the back with <F, U>. It still preserves EO because it's the same moves just different angles
 
Doing an F move or doing a y' R' is literally the same thing from two different angles, so it doesn't change EO at all. It's like doing Petrus F2L with the 2x2x3 in the back with <F, U>. It still preserves EO because it's the same moves just different angles
LL edges yes but for F2L edges it doesn't preserve EO to rotate and take it out. Saving a rotation is better in either case.
 
Say you have a last slot case where the pair can be inserted with R U R', and you can see that you will get a dot OLL. What is an alg to orient all of the last layer edges?
In most cases, it's going to be faster to just R U R' and take the dot, assuming you're not super trash at the dot cases. That being said, you can do :
R U' R' U2 M' U R U' r' to force partial EO
 
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