Learn Farsi: بچه مریض است.

In Farsi, being sick (mariz) is treated as a standard adjective describing the subject, just like in English. So you use the normal 'to be' verb (ast). The impersonal enclitic structure (like sard-am ast or sard-esh ast) is generally reserved for physical sensations (hot, cold, hungry, thirsty) and mental states, rather than general illnesses.

How would this sentence sound in everyday spoken Farsi?

In conversational Farsi, the verb ast (is) usually shortens to an -e sound attached to the end of the previous word. So, bache mariz ast becomes bache marize.

Does bache mean baby or child?

It can mean both! Bache is a very common, everyday word for a child of any age, including a baby. If you need to specifically emphasize that it is an infant, you can use nozâd, but bache is perfectly natural here.

There is no word for 'the' in this sentence. How do we know it means 'The child' and not 'A child'?

Farsi does not have a direct equivalent to the English word 'the'. A noun at the beginning of a sentence without any indefinite markers (like an -i at the end, or yek before it) is usually understood as definite based on context. If we wanted to say 'A child is sick', we would say yek bache mariz ast or bache-i mariz ast.