Yes that is the actual site.

LuckyPatcher has been around forever,
and has a good reputation + community.

Never seen anyone mention anything that it might contain malicious code.

The developer receives revenue through donations and showing ads on the site.

Sadly the project is not open source though.
My guess would be to prevent the hacks / patches it uses,
from being patched / made un-usable.

To be 100% sure though,
you'd have to de-compile the app,
and reverse engineer the source code,
which is a very tedious and time consuming task.

You'd want to see the source code, to verify it does only what it claims.

That said, I used it maybe 10 years ago, on a firewalled/monitored device, and it didn't make any outbound connections back then, ever.

for youtube, just use revanced.

and yeah custom patches sometimes don't work, that's pretty normal tbh

Lucky Patcher is interesting but much like rooting my phone, I found it disappointing in that it didn't bring much that I really wanted to do on a phone.

If you want to hack games, just use cracked stores like happymod.

Edit: With HappyMod you are risking the potential for malware as some people have mentioned. Do your research before trusting an internet stranger.