Help me to finde a Action Cam

I'm interested in the results of this question, as well.

Some GoPro? I can't help you with Cameras sorry :(

You're welcome

Besides not sure if chinese copycats are good equipments

Edit: found a Xiaomi 'Yi' EUR 54,99 on Amazon,

I have this one, it's ok for me but you might not agree I dunno
https://www.amazon.com/TEC-BEAN-Waterproof-Wide-Angle-Rechargeable-Accessories/dp/B01N7JS6IA

it's good that it comes with 2 batteries, full waterproof plastic case and bunch of different mounts for everything from helmet or bike rod to your belt.

I was lucky enough to get a Yi4k courtesy of a giveaway by the makers of Liquivid software. While thats specific model may be above your stated needs, its certainly a strong brand for features vs price compared to others and seems to be a tough sod as well (having done gig photography for some time, that tends to be something I notice), so... maybe one of their lower models may suit?
Battery life has been good enough that while in storage (or "lost" as i thought) for 3 months, the battery still had an 80% charge! O____o

Additionally (as ill be using it in a music video shoot soon) i have found there are a lot of budget accessories available that have positive reviews.

Generic sales page: https://www.aliexpress.com/store/3050005
Actual website: https://www.yitechnology.com/

EDIT: However, for your needs (unless you're really needing to helmet / chest mount etc), any samsung compact with a schneider lens should do nicely also.