I'll give it a try
I also learn Polish and this way I can practice a little bit.
>żiem
The 1st person singular of żyć (to live) is żyję.
This means "to live" as in "to be alive". I'm not sure if you can use it for locations though. Probably it would be better to say "miezskam", which means "to live" as in "to reside".
>(in Vilnius)
Vilnius = Wilno
in Vilnius = w Wilnie
>Chciem
Once again, the 1st person singular of "chcieć" is not "chciem" but "chcę".
>po polski
This should be "po polsku". "Polski" needs to be in the dative case.
>to jest pierwszy moj zdanie
Hmm... zdanie (sentence) is a neuter noun, so you'd need to use the neuter singular nominative form of "mój", which is "moje". Likewise, "pierwszy" should also be in the neuter form ("pierwsze"), with the posessive pronoun before it. Therefore "to jest moje pierwsze zdanie".
> Teraz użiwam pomoca
I suppose you mean something like "now I could use some help", right? I'd suggest something like "Potrzebuję pomocy" (I need help).
Regarding the title of the thread, I think it should be "Chcę się uczyć języka polskiego" (I want to learn the Polish language). "Języka polskiego" is the genitive of "język polski". I'm not sure if you can use a "po + <language>" construction after "to learn", but if you can, it'll have to be as explained above ("po polsku").
Now we wait for a Pole