Can I add Ubuntu fonts to website? What are licenses of those?

Short answer: Yes. Ubuntu comes bundled with "open" fonts that are free to distribute.

Long answer: There's a LOT of information about each individual font's license. Depending on what package the font is a part of and that package's license is, certain restrictions may apply, but as a general rule of thumb you can use the default fonts that come with Ubuntu.

If you'd like info on the Ubuntu fonts themselves (Ubuntu Bold, Ubuntu Italic, etc.) you can find all of that here.

According to this font makers homepage: http://linux.thai.net/projects/thaifonts-scalable

it is free; "License: This package collects Thai scalable fonts available in free licenses."