Learn Polish: Podsumowując, astronomia to bardzo ciekawa nauka. - In conclusion, astronomy is a very interesting science.

It is a present adverbial participle (an "-ing" word) created by adding -ąc to the stem of the imperfective verb podsumowywać (to summarize). Literally meaning "summarizing", it acts here as a fixed discourse marker to mean "in conclusion" or "to sum up".

Could I use ostatecznie instead of podsumowując in this sentence?

They do not mean exactly the same thing. Podsumowując is used to gather and summarize points you have just made ("in summary"). Ostatecznie means "ultimately" or "in the end", which usually implies reaching a final decision or outcome after a long process or debate.

Why is ciekawa nauka in the Nominative case here? Doesn't defining what something is require the Instrumental case?

It depends on the linking word! Because the sentence uses the pronoun to as the linking word instead of the verb jest, both nouns must take the Nominative case. If you used the verb jest, it would indeed require the Instrumental: astronomia jest bardzo ciekawą nauką.

Is the comma after podsumowując strictly necessary?

Yes. Under Polish punctuation rules, expressions built with adverbial participles ending in -ąc (like this one) must be separated from the main clause by a comma, especially when they act as an introductory phrase.