"I like to eat borshch."
Translation:Я люблю їсти борщ.
Is it always necessarry to have the subject? Can I omit it in this sentence?
'їм' is the first person (present) participle for the verb 'їсти' (to eat). So, I eat borshch (or, I am eating borshch) is 'я їм борщ'. Using the form 'я люблю' (I like) means the verb takes the infinitive form, as in English. So, I like to eat borshch is 'я люблю їсти борщ'.
In a similar fashion, you can use the auxillary verb forms of хотивати (to want) with the infinitives for to drink and to eat. For example: I want to drink juice is 'я хочу пити сік'; I want to eat meat is 'я хочу їсти м'ясо'.
I hope you can see the difference now.