"Raj does not eat in the afternoon."
Translation:राज दोपहर में नहीं खाता है।
You can drop the है in this sentence. The rule is that in any present tense negative sentence, है is optional. The only exceptions are sentences that have no other verbs (like वह बड़ा नहीं है ) where it cannot be dropped.
The negation can come either before or after the main verb (it has to be directly adjacent though). Placing it before is the standard form and it is placed after the verb when you want to emphasise the negation.