Hi, Sam. I'm native speaker of Japanese.

"My sister is a dancer, she is studying dancing."

can be translated as

「私の妹はダンサーです。彼女は踊り（おどり）を勉強しています。」.

"My" is also translated as 僕（ぼく） or 俺（おれ）.

"sister" can be 姉（あね）if she is older than you.

Nowadays, most Japanese use the word 「ダンサー」　when they mean "dancer" .

If the dancer is young girl, there is a expression 「踊り子（おどりこ）」which means the girl who dances.

踊り子sounds antique. There is a famous novel 『伊豆の踊子』 translated as "The Izu Dancer" by Yasunari Kawabata, the nobel prize winner.

"I work part time/ I have a part time job."

can be translated as

「私はパートで働いています。」or 「私はアルバイトをしています。」

although there is no clear difference between パートand アルバイト, when the speaker means part-time workers who are young people such as students,  the word アルバイトis mostly used. On the other hand, when the speaker means part-time workers who are house wives, the word パートis applied.

アルバイトcomes from the German word Arbeit, which means labor, and パートcomes from English expression "part-time job".

わたしis usually used by women. This is politer than 僕andおれ. Men also use わたしwhen they talk to their boss or the people who are not familiar to them. 私is used in written languages and public speech.

僕 and 俺are used by men, mainly young men. 僕 is more polite than 俺, and also used in a bit broken written languages such as e-mails or blogs.

俺 is unpolite one. teenage boys begin to use the word.

in addition to above mentioned three, there are many translation of "I" in Japanese such as わたくし、うち、わし、吾輩etc, etc...

I hope this comment can help you learning Japanese!

thank you this helps a lot :D

would the sentences be

私のいもとはおでれさん　彼女はおでれはべんきょします