SUM of values in a comma delimited cell

Thank you all for thinking on this!

I was trying to figure out and try various solutions presented by you.

So what I would have in cell A1 would be A,B,C. ("A,B,C" is if there is just three. There could be less or more than 3, ie "A,B" or "A,B,C,D" etc.)
In B1, I would like to see however many letters are delimited in A1 to be shown as A+B+C, or if there were 4 letters show up in A1, then B1 would show A+B+C+D.
Then in C1, if I define under the "Insert Name" command that A will always be the value I enter in, say, E1, B will be the value I enter in F1, C will be the value I enter in G1, and D, will be the value I enter in H1, etc, then in the case of A=1, B=2, C=3, and D=4, I want to see the number 10 in C1.

Is this all possible with formulas?