Will my AI algorithm for a python checkers game work and if not, what others should I consider?
You're on the right track, and another answer already has lots of details, but one thing I want to highlight is that you should focus on evaluating positions rather than evaluating moves. The value of a move is simply the value of the position it ends up in.

Instead of awarding lots of points to a "winning move", you award lots of points to a won position.
Instead of awarding some points for a capture, and some more points for a king capture, you can score positions according to material. The reason we consider a capture a good move is because it deprives the opponent of pieces. Acquiring a king improves our own material. Evaluating positions on material takes these things into consideration.
Likewise your rules about control of the center, being against the wall, etc. are much easier to do (and work better) as evaluations of a position, rather than tallying up points for "moves that result in X".

Win/lose/draw are "hard" conditions; if the game is over, it doesn't matter how much material you have left, or where it's placed, or anything else. You wouldn't choose a draw over a win just because the win sacrifices a piece. Evaluation rules for material, mobility, etc. are "rules of thumb" for how close a player is to winning, or how much ability they have to win, so you only really care about them when you don't have a forced win/loss/draw within your search horizon, and when you do use them, you want them to produce scores that are as similar as possible to the scores you would get if you could search every position until the end of the game.
You can start out assigning scores to your different evaluation rules by intuition, but to make them really good, you would simulate lots of games to the finish, and then run statistics on the winning and losing players' positions — then you would assign higher scores to the rules that most strongly correlate with positions that actually win.
I'll open with saying I'm not a data scientist or statistician so I've been trying to figure out the best way to score a set of given AI moves to help the computer determine which move path to choose. I've come up with the following and am asking if there is a better way to do this or if this will even work in the first place.
For any given player:

Normal move +0
Capture normal piece +1
Capture king +2
Move resulting in king +2
Win game +10 (Should make AI highly prefer this path unless another provides a stronger and safer short term advantage.)
Draw Game (Disregard path unless it's the only remaining option. Static 1 Goodness Point.)
Lose Game (Disregard path unless it's the only remaining option. Static 0 Goodness Points.)

I'm also toying with the following:

Move that ends against a wall +0.5
Move that gains center control without threat +0.75
Move that results in potential capture of multiple AI pieces (per piece) -0.25
Move that results in piece getting "stuck" (within 1 turn) -0.5

The AI then runs through X levels (Let's say 4) of moves deep in the search tree and tallies points for both the player and opponent for each branch.
I track the following (per branch):

Total points for AI
Total points for human opponent
Opponent likelihood of choosing branch (see below)
Branch "Goodness" (see below)
Total branches (move combinations)

In order to choose the best one, here is the algorithm I have developed but haven't determined if it will work well yet:
Base Opponent Move Probability = 100 / Total Branches * (Human Opponent Points Gained + 1)
Player Branch "Goodness" = Human Opponent Probability * Total Points for AI Player
The AI then chooses the move branch with the highest "Goodness" points or picks one at random in event of a tie.
Example:
4 Branches Available. In one of them, the human will king once and the AI will capture 2 pieces and king once.
100 / 4 Moves * (1 Opponent Points + 1) = 50 Human Opponent Likelihood Score
50 Human Opponent Likelihood * 5 AI Player Points Gained = 250 Move "Goodness" Points
The only other thing I can think to add would be to score the entire board's "favorability" at the end of each branch and multiply that by the "Goodness" Score. Favorability meaning the total point score for all pieces, kings, center/wall control as a given end state. Though the more I expand on this the more it seems like I should pick one or the other. Either score as each of the moves in a branch are calculated or score the end board favorability result of each branch, not both.
Maybe something like: (Board Favorability / 2) * Goodness = Final Branch Value
Regardless, am I on the right track here? Will this approach work (not the favorability part, the general scoring and "Goodness" score for a given branch) or am I on the complete wrong track? Thanks for any assistance!