No. This is not the way.
> give parents the ABILITY to advertise the users age to browsers, apps and everything in between.
Accounts and Applications to services that provide countent are set to a country-specific age rating restrictions (PG, 12+, 18+, whatever). That's it.
None of the things you mentioned have any point to concern themself with the age or age-bracket of the user in front of the device. This can and will be abused. This is very obvious. Think about it.
That is what I meant by age(-rating), you are correct. However, drop country specifics - too complicated. Age brackets are enough: child, preteen, teen, adult. At around 16-17 these should be dropped anyway since at that point people are smart enough to get around these measures anyway and usually have non-parent controlled devices.
Why should the applications get to decide if they are appropriate for a particular age? Shouldn't that be up to the parent? I shouldn't need to tell my kid: "Well, to use this compiler software, you need to set your age to 18 temporarily, because some product manager 3,000 miles away decided to rate it 18+. But, set it back to age 13 afterwards because you shouldn't be on adult sites." It's stupid.