The sentences are correct. What you are seeing is the English subjunctive mood, required by the verb (and others like it) "suggests that he..." followed by the infinitive without the "to."

Which sounds better to you:

1. He ordered that the report is here no later than 7 PM, or

2. He ordered that the report be here no later than 7 PM? (Pick this one)

You could even recast, correctly, as:

He ordered the report to be here no later than 7 PM.

We don't see the subjunctive that often in English, but do in many other languages, at least the ones I know.