Is it legal to use Youtube Data API to create youtube-like app that aggregrate youtube videos from any channel?
Your question is answered in the first paragraph of the YouTube API Terms of Service.
1. Is it legal to use Youtube Data API to create youtube-like app that aggregrate youtube videos from any channel?
The terms don't prohibit it, as long as the client is compliant with the ToS. So, yes, it is legal.
2. Can I (legally) monetize those app with Admob?
It depends.
You agree not to use the YouTube API for any of the following commercial uses unless You obtain YouTube's prior written approval: [...] the sale of advertising, sponsorships, or promotions on any page of the API Client containing YouTube audiovisual content, unless other content not obtained from YouTube appears on the same page and is of sufficient value to be the basis for such sales.
I'm not an expert in law questions, but what this says (imho) is that you may advertise your application if it does not solely contain YouTube content. In other words, your application has to extend the functionality of https://youtube.com, not recreate it.
In any case, you may not block or in any way alter in-player ads.
Conclusion
Based on the short concept of your app you posted in the question, I would say:
- You may build "youtube-like app that aggregrate youtube videos from any channel", but
- you may not advertise it, since it does not feature original content.