syourai watasi ha kagaku no kenkyuusya ni naritai desu.

The particle は marks 私 as the topic (“As for me…”). In Japanese, once it’s clear who you’re talking about, you can drop 私は and still say: • 将来科学の研究者になりたいです。 Omitting 私 makes it more conversational; including it adds clarity or emphasis.

The particle の links two nouns, showing a possessive or descriptive relationship.
• 科学 = “science”
• 研究者 = “researcher”
Together 科学の研究者 = “a researcher of science” (i.e. scientist).

Because the verb なる (“to become”) takes its resulting state with に. The pattern is:
• X が Y に なる
Here 私 (implied subject) becomes 研究者 (marked by に). An object marker like を would be ungrammatical, since なる is intransitive.

• 研究者になる = “to become a researcher.” It’s just a plain non-past statement.
• 研究者になりたい = “want to become a researcher.” The suffix ～たい attaches to the verb stem (なり) to express desire.

Grammatically, なりたい behaves like an い-adjective (“wanting to become”). In polite speech you add the copula です to soften it: • Casual: なりたい
• Polite: なりたいです

Yes, 科学者 (かがくしゃ) is the standard word for “scientist.”
• 科学者になりたいです。
However, 科学の研究者 emphasizes “researcher in the field of science” and illustrates the A の B structure. Both are correct; 科学者 is simply shorter.

Yes. Japanese is fairly flexible as long as the verb stays at the end. Common alternatives: • 私は将来科学者になりたいです。
• 将来私は科学者になりたいです。
Putting time expressions (like 将来) at the front is just a common stylistic choice to highlight “in the future.”