1) The sentence A is correct and better translation for the English sentence. The sentence B should be 私は日本語の練習が必要です. 練習 is a noun here. The の in the sentence modifies the noun, 練習. So the direct translation would be "I need Japanese practice."
2) Both are correct. The sentence A uses polite form. You can use polite form when speaking and writing. The sentence B uses plain form. This style is used in formal writing. It is better to use polite form when speaking, because plain form speech may sound unfriendly. Oh, and you can say 今週末 instead of この週末. 今週末 sounds much more natural :)