For example when you first time in real life meet some person and you want be sure that this is correct person:
- Cześć, to ty jesteś Tomek? (Hello, you are Tom?)
- Tak, cześć/witam (Yes, hello/welcome) - in this situation hello will be better word.
First part it is answer and second is greetings.
This is quite a strange word in Polish. For example you can either say "Witaj!" (kinda like "you be welcome here"? hard to translate...) or "Witam!" ("I welcome you here"). I think it should rather start the conversation than be an answer to "May I come in?". I'd rather imagine "Tak, tak, oczywiście, zapraszam" (yes yes of course, I invite") as an answer here ;)
Moreover, as "witam" should rather be said by the host, it somehow shows an uneven relation, where the person saying "witam" is higher. For example, it is a common mistake for which students may get scolded, to start an e-mail to a university teacher with "witam". That may be considered impolite. Generally it's hard to use by a person non-native to the culture, and it's hard to describe its usage. I feel that I may have rather confused you more rather than explained something... maybe someone can answer that better.
A response equivalent to "you're welcome" would be "Proszę bardzo", also "Nie ma za co" (There's nothing to (thank) for" or "Ależ proszę" (slightly old-fashioned).