i've been wondering, would there be somebody who knows how
to plugin a WhoIs or a domain check availability box within
a html-based website?
A domain name check or whois tool requires a whole backbend script to run. So it isn't as simple as plugging it in. It all depends on which service you want to query. Also, if you have a domain reseller account, chances are that the company offers an API. However, the whole situation requires some intermediate programming.
It's not really possible to just "plug-in" a whois/domain interface -- unless you can find a remotely hosted one, in which case that would be provided by a company that will redirect your traffic to themselves.
You need to be a little more specific as to what you're looking for. Do you want to make money from domains? Do you have a reseller account? Do you ant to sell the domain, once someone has done a search? Or, do you just want to offer a domain check service?