I know there are some alternatives for Helvetica Neue for web usage, but i want to ask, if it is legal to use Helvetica Neue on some commercial website.
This font is commercial property and is not allowed to use without proper licensing for usage.
You may consider alternatives to the Helvetica Neue, like the ones listed here http://theultralinx.com/2013/03/5-google-web-font-alternatives-helvetica-arial.html
To clarify, there are two different licenses: desktop and web.
If you have the font on your desktop (legally) you can create graphics for your site with it. You can even specify it in your CSS with fall backs so that it displays for those who also have it on their desktop but degrades gracefully for those who don't.
When you choose to embed the font on your site so everyone can see it with @font-face you'll need the additional licensing complexity for the web.