Effect of +I on the alpha hydrogen in aldol reaction
Is the alpha hydrogen acidic enough to react with base?

The answer is yes. As you said +I effect of the methyl group stabilizes the carbocation. It is weakly acidic but not weak enough to not be taken by any base.

Will it proceed through aldol reaction or will Cannizzaro reaction occur?

It will proceed through Cannizzaro mechanism even though it has an alpha hydrogen. That is because if you take it through aldol, the attacking nucleophile in the second step is $\ce{-C(CH3)2(CHO)}$ which is a very bulky nucleophile and so it isn't able to attack on $\ce{CH(CH3)2(CHO)}$. Think, if this reaction undergoes than the product will have $\ce{CH3}$, $\ce{CH3}$, $\ce{CHO}$ and $\ce{-C(OH)(CH(CH3)2)}$ groups all on one carbon. The steric crowding will be so immense that the reaction becomes infeasible. That is why it undergoes Cannizzaro reaction which has $\ce{H-}$ as the attacking nucleophile (in the second step).
I think your other questions won’t arise if you think this way.