"I also want to eat the borshch."

Translation: Я теж хочу їсти борщ.

[Sushinese]

"Also, too" is expressed by the
same word теж in Ukrainian!
And isтеж always positioned after a subject?

[skstudio]

"Теж/також" are adverbs. Adverbs are often (not always) placed before the corresponding verb (in this case "хочу"). In general, Ukrainian has a flexible word order.