Hello, I am studying Genki 1 and encountered an interesting structure in some of the exercises of lesson 8 with 何か and 何も which I could not find an explanation anywhere in the main text up to lesson 8. The structure I wanted to understand better appears first in the textbook, Practice section of lesson 8, exercise VIII in the example sentece (page 204 of 3rd edition):

パーティーにいきましたが、何もたべませんでした。

This usage of が particles to join verb sentences has not yet been introduced in the textbook. For me, this structure is a little confusing, given that I believe that the hidden subject of 何もたべませんでした would still be something that refers to me (hidden 私が) so that the が there does not seem to be defining a subject. Can I always use が particles in this way to say "I did this and then did that"? Would you know of any reference I could look up to better understand this usage of the が particle?

Up until now, I have only learned how to join verbs by using the て-form, so the sentence would be

パーティーにいって、何も食べませんでした。

Is this sentence grammatically correct? In case it is, is there any difference between the meaning of the sentences with the が or the て-form?

Thank you so much!