Greetings Rockhounds! I found this big rock about a month ago, but i know nothing about it. Have in mind that 2000 years ago, this place was fully covered by sea, it was a Persian army Harbor, and to be more specific, it was Xerxes´s Harbor. So, maybe these engravings are just signs from sea plants or animals? To be honest, it reminds me Jasper, but I can not be sure.

Also, tell me please, do you know what are these blue mineral layers that i find, always glued to simple stones? They are everywhere.

And last, tell me please, what is this reddish stone in the last picture?

As you can see, I am relatively new, so I really want your help in many things. Happy to ask for it!

I agree, the Big Rock looks like an "agatized" or "fossilized" coral.  Very nice looking specimen.
The blue "coatings" look like blue chalcedony.
Here's a good article that may help,
https://www.rockngem.com/blue-chalcedony-a-lapidary-superstar/

And the red looks like it may be andradite garnet on quartz or calcite, especially if you live near Serifos Island. The calcite would scratch easily with a knife, quartz won't leave a scratch.
Looks like you have a good eye for rocks!