Learn French: Le ministre déclare que le scandale est choquant. - The minister declares that the scandal is shocking.

Because the introductory verb (déclare) is in the present tense. In French reported speech, if the main verb is in the present or future, you don't change the tense of the reported words. The minister's original direct quote was simply: 'Le scandale est choquant.'

In English, we can say 'The minister declares the scandal is shocking' without the word 'that'. Can I drop que in French?

No, you can never drop que in French. When connecting an introductory verb like déclarer or dire to a reported statement, you must always use que (or qu' before a vowel or mute H), even when English skips 'that'.

Choquant looks a lot like an English '-ing' word. How does it work in French?

Choquant is a present participle, coming from the verb choquer (to shock). Just like in English, French present participles can often be used as adjectives. When used this way, they act like normal adjectives and must agree in gender and number with the noun they describe. Here, it is masculine singular to match le scandale.

Can ministre be used for a religious minister, like in a church?