Now I just have to ask is there a limit which asic can mine or not?
No, you can use any ASIC that can mine Litecoin.
After my miner connected to the pool -there is a not-authorized message in the history log.
I’m registered and use of course the strings out of my profile.
Make sure that you entered your worker's name and password exactly as on the website. In particular, keep in mind that they are case-sensitive. Feel free to send a screenshot of your miner's configuration page to support via email to make sure all parameters were entered correctly.