Do I need to inform the user about storing the score locally?
No, there is no need as long as you don't transmit, store or process any personal info. It's doubtful that the score could be considered personal info, but you're not sending it to your servers in any way, so you don't seem to be processing it anyway.
Do I need consent for using non-personal AdMob?
You have to check this with AdMob, but usually, if it is non-personal, they shouldn't be processing any PI, so you're clear without informing.
Do I need to ask for the age? How should I handle kids?
Again, you're not processing any PI, so regarding GDPR there isn't any problem.
Can I disallow a user from using the app if consent is not given?
If you needed consent, no, it would be unlawful to block a user for not giving consent, unless it is impossible to provide the service without it. See recital 43:
Consent is presumed not to be freely given if [...] the performance of a contract, including the provision of a service, is dependent on the consent despite such consent not being necessary for such performance.