Finding time complexity of my solution to the 'longest palindrome' problem in Python
Some thoughts on the long version only:


Use at least one linter like pycodestyle on your code to learn to write more idiomatic Python. This makes the code easier to read for other Python developers.
Most of the names are good (longestPalindrome), but


index, i and findcharIndex in a single method is very confusing,
the semantics of A, oList, j and Solution all have to be inferred from context which is mentally taxing, and
type suffixes like in remString are generally discouraged.

if foo then return true else return false should be replaced with simply return foo in any language.
Ideally your algorithm should not need the if(longestPalindrome == ""): check at the end - longestPalindrome should contain the longest palindrome by then.
Many @staticmethods is a common anti-pattern indicating that the code is really imperative rather than object oriented. This code might work better as a @property of str, since semantically that is what it is.