As I said, the Apple ID age does not limit anything else. What is not fun about he age? It should not prevent you fro doing anything other than those 2 things. And Betas are an entirely different issue.
Its really not recommended to participate in Betas, unless you know what you are doing and are ready to deal with issues stemming from the usage of betas on your own and are prepared to have a bricked unusable device. Betas often will have issues, some of them device breaking and Apple will not help you. You will be on your own with such issues., and may need to restore the device to factory settings and not use any backup, losing any and all data on the device. Betas are not a wya ot have fun or access OS versions early. They are meant as a development tool.
Apple offers no support or help for betas unless you are an actual registered developer, and for that you need to be 18 or older.
Note the following:
Apple Beta Software Program
Is the public beta software confidential?
Yes, the public beta software is Apple confidential information. Don’t install the public beta software on any systems you don’t directly control or that you share with others. Don’t blog, post screen shots, tweet, or publicly post information about the public beta software, and don’t discuss the public beta software with or demonstrate it to others who are not in the Apple Beta Software Program. If Apple has publicly disclosed technical information about the public beta software, it is no longer considered confidential.
Read our Terms for full details
No Support and Maintenance; Future Products. During your participation in the Beta Program or in a particular seed, Apple is not obligated to provide you with any maintenance, technical or other support for the Pre-Release Software. If, at Apple’s option, such support is provided, it will be provided in addition to your normal warranty coverage for your computer and/or device. You agree to abide by any support rules and policies that Apple provides to you in order to receive such support. You acknowledge that Apple has no express or implied obligation to announce or make available a commercial version of the Pre-Release Software to anyone in the future. Should a commercial version be made available, it may have features or functionality that are different from those found in the Pre-Release Software licensed hereunder.