Regarding the L4C: obviously there's the "Permute the Orient", which is essentially a fleshed-out version of your first-post example. The step-3 algorithm you posted has a inverse which cycles in the opposite direction, you'll find a combination of these two can sort out any permutation case. And Susie's previous post links to Orientation algs ...
I think an intuitive beginners choice is:
F D' F' R' D' R ( U or U2 ) R' D R F D F' ( U' etc)
Note that you don't need to learn the inverse of this alg, just rotate the cube: y2 z
The two-look simplifications of L4C are mentioned on the Wiki page:
https://www.speedsolving.com/wiki/index.php/L4C and
https://www.speedsolving.com/wiki/index.php/L3C
... they're OK for the 36 awkward cases where one corner is in the right place but not oriented, and the remaining 3 corners need cycling. If you know all 18 3-corner cycle algorithms ( 9 and their inverses) you can use a combination of two of them to (1) solve one corner; (2) solve the remaining 3 corners with one of nine 3-corner cycles:
Simple example: On a solved cube, do:
L' U R U' L U R' U' y2 L' U R U' L U R' U'
then solve with:
U R U' L' U R' U' L y2 U R U' L' U R' U' L
the first step solves the Back-Right corner whilst disturbing the F-L corner, second step will be one of the 9 counter-clockwise L3C cycles.
There are other variations: but the first step has to move the in-position corner, whilst solving another corner. I'm guessing this is too advanced for you at the moment.
I really like Mirrorblocks, but I'm no expert, so please read other people's replies.
And you have to try it 'unsighted', solving by tactile means alone.