Forbedring min norsk (not really sure what you're trying to say here, literally says "Improvement my Norwegian". Please note that there is no present continuous tense in Norwegian, and that the suffix "-ing" only is used in nouns - just like the suffix "-dom" in "freedom" or "-ment" in "appointment" etc. If you wanted to say "Improving my Norwegian" you could, for instance, write "Forbedrer min norsk", or even better "Forbedrer norsken min". In my opinion, phrases with the possessive pronoun (here: "min") in front of - in lack of proper grammatical jargon - the possession (here: "norsk") sound a bit Danish or very formal - some people might even find it a bit archaic. In most cases, it would probably sound better if you put it after, but please note that in that case the noun needs a definite article (like "-en" in "norsken") at the end)

Jeg øver hver dag. Jeg heter Samantha. Jeg kommer fra Amerika. Når jeg har barn (in Norwegian, this sounds like "Every time I have children", so in order to express that this is something that might happen in the future you would use the verb "å få", which would be "Når jeg får barn, [...]" in your sentence here), jeg ønsker å lære dem norsk (these two words need to change places. I'm afraid I'm not able to give you an adequate explanation why this is so, but it's probably partly because it's a clause. Correct: "[...] ønsker jeg å lære dem norsk.") . Så jeg må lære (I guess you meant to say "therefore, i have to learn it", which would be "Derfor må jeg lære meg det."). Jeg har hunden (in this case you would say it in Norwegian the same way as you do in English, with an indefinite article: "Jeg har en hund"). Han heter Snowball. Jeg elsker ham (this is actually very good - even most Norwegians can't get this right).

Hope you don't find my long comments discouraging, because I thought this text was pretty good :)