Is the tax credit for donations to a public school in Arizona $200 or $400 for single filers for 2018?

An individual may claim a nonrefundable tax credit for making contributions or paying fees directly to a public school in this state for support of extracurricular activities. The public school tax credit is claimed by the individual taxpayer on Form 322. The maximum credit allowed is $400 for married filing joint filers and $200 for single, heads of household and married filing separate filers. 

If contributions are made to other organizations (ie Firefighters charity), does that have an impact on what I can donate to AZ public schools?

No, the contributions do not affect each other. 

Note, however, that these are all nonrefundable credits, so once your assessed tax has been reduced to zero by various credits, additional credits will have no impact. If the contribution to one charity reduces your assessed tax to zero, then any nonrefundable credits for another charity will be lost.