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I use for the cases of 1-5 one my old algorithm and two variant thereof. I found that these algs has the properties for rotation of corners.
These algorithms earlier I used for permutation of corners - https://vk.com/doc185254069_229875947
For case 6 I also used Sune and Anti-Sune algs.

Note for the LCase alg on http://lubixcube.com/CMLL.html
For the LCase you can use the back alg for Blinkers (i.e. F R' F' R U R U' R').
For example do the Blinkers alg (R U R' U' R' F R F') on the solved cube => We get LCase. Now do back alg (F R' F' R U R U' R') for get the solved cube.

Corner Orientation Algorithms
Headlights (U): F (R U R' U') F'
Bruno (Pi): F (R U R' U') (R U R' U') F'
Double headlights (H, & Double sune): F (R U R' U') (R U R' U') (R U R' U') F'
L case (Bow tie, Triple sune): F R' F' R U R U' R' (back Blinkers alg) - 8 steps
Blinkers (T, Chameleon): (R U R' U') R' F R F'
Sune: R U R' U R U2 R'
Anti-Sune: R' U' R U' R' U2 R

Corner Permutation Algorithms
J perm: (R U' L U2 R' U R U2 R' L') +U - 11 steps
Y perm: (R U' L U2 R' U L')*2 + U/U' - 15 steps (this alg from Eygeny Benek aka Lenon)

Note for the LCase alg on http://lubixcube.com/CMLL.html
For the LCase you can use the back alg for Blinkers (i.e. F R' F' R U R U' R').
For example do the Blinkers alg (R U R' U' R' F R F') on the solved cube => We get LCase. Now do back alg (F R' F' R U R U' R') for get the solved cube.