Here is my problem

How to get that logs-folder back and how to open the files inside on a pc?

did you tried ?

Yes, now

No success. It only shows the later created logs-folder inside .yappari - but thats not the one i lost with ´mv logs /home/user/MyDocs´- I think I missed ´/´ at the end of Mydocs and now it got lost ´somewhere´ or is damaged , is that possible?

Inside MyDocs is a "._" (whatever it is, I can´t enter with cd) and a Trash-1000-folder....

Would be interesting what was inside the now missing logfiles - but if its not possible to get them back, can I remove the ._-´file´ and the thrash-1000-folder anyhow/check whats inside them?

Trash-1000 seems to be empty except 3 folders...

it is irrelevant if you put / at the end of the path or not in that mv, it will be mv properly anyway.
That ._ is a Mac related, self created folder, should not content nothing but junk. Did you tried checking the content of those two folders as root? Maybe playing with chmod/chown will get you access.

You could install recovery-tools package and run testdisk to look for the erased files or folders.

This is a crazy idea but... Did you by any chance run that´mv logs /home/user/MyDocs´ with the phone connected to the PC in the USB Mass Storage mode? If so, try the Mass Storage mode again and see if the folder magically reappears. You will need to check it on the phone though, not on the PC.

Regarding your other two questions. Yes, you can delete '._'. It is something to do with Mac, IIRC. If you do not use a Mac, you do not need it. To be honest, I am not sure if you need it even if you do have a Mac. All I know is that I deleted it years ago, along with other Mac related files (sorry, for the life of me I can't recall their names now) and never missed them.

The Trash-1000 folder is a Linux equivalent of the Windows Recycle Bin (more correctly, not Windows but Windows Explorer and not Linux but Nautilus, but we do not need to split hairs). In other words, it is a temporary repository of your deleted files. Have a look what's inside and if nothing important, feel free to delete it.