Prime checking and factorization with just bit cheking
Given any specific candidate divisor $d$, it is easy to check whether $d$ is a divisor of the number (the standard modular reduction algorithm is a generalization of those tricks you mentioned).  This can be done for all $d$.  However, it doesn't help with efficient factorization, because there are exponentially many candidate divisors, so trying each one, one-by-one, is far too inefficient.

In other words, this approach to factorization is not likely to be useful, no matter how many tricks you accumulate.