Can I use different P-values when comparing different groups for the same variable?

Did you mean different significant levels? P-values cannot be used, they are calculated. Significance levels such as alpha=0.05,0.01 are chosen by the user.
When comparing different groups for the same variable, it is better to use the same significance level such as .05.
Should you wish, you could compare them all again with a different significance level such as .01.