1). Yes, but more correctly:
A free electron pair of the carbonyl oxygen attacks on the proton and then, the free electron pair of the primary amine group attacks on the carbonyl carbon, ..etc.., followed by cyclization and final departure of the catalytic proton.
2). It is obvious and easily understood that protonation of the primary amine group, blocks its free electron pair and inhibits cyclization that way, according to the above mechanism.
On the other hand, creatine is a strong tribasic compound (strongest basic group pka = 12.43, ChemAxon), as being a guanidine derivative and has an order of functional group basicity: imine > tertiary amine > primary amine.
Consequently, the primary amine group can be protonated in high proton concentration, only and which is translated to low pH.