I agree. In English food is uncountable and therefore doesn't need an article so either 'the food' or 'food' is acceptable as a translation as we don't know the context.
Yes, but there is a difference in meaning even in English between "looking for food" and "looking for the food." Inclusion of the word to in the Czech sentence indicates that "the" or "that" should be part of the English translation.
As a Serbian, I find this confusing because of "to", which in Serbian means "that" and we don't have articles. This kind of statement would usually be complemented with finger pointing or something similar. Would "Matěj hledá jídlo" be a valid sentence? Would it have a different meaning?
It would be just "Matěj is looking for the food."
"To" here points to some particular food that has been already mentioned.