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Regarding 1, see the answer of

Regarding 2, which factorization would you expect ?

Regarding 3, you ar lucky because in the tree of the representation of the expression, alpha+beta appears as subtrees, so the following works:

sage: U1.subs({alpha+beta:1})

Regarding 4, if you are using jupyter notebook, you can add the following in the first cell:

%display latex