The following website should help with passes https://www.fs.usda.gov/main/cleveland/passes-permits If you have an Adventure Pass, you should be good for any parking and hiking that you want. There are a few exceptions but the general guideline is the adventure pass will get you in to any national park or forest. The adventure pass is also good for certain campsites if you're into that sort of thing as well. You can always call up the local ranger district and they should get back to you in a day or two about any particular questions that you might have. I have the access pass which is very similar to the adventure pass and I use it in Cleveland National Forest quite a bit. Hope this helps!
Yes, a national parks pass is generally good for all Federal lands.
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