Learn Italian: Penso che questo sia un indizio importante. - I think that this is an important clue.

Penso che (I think that) expresses an opinion. In Italian, verbs of opinion, belief, or doubt require the subjunctive mood in the following clause. Sia is the present subjunctive form of essere (to be) for the third person singular, agreeing with questo (this).

In English we can say "I think this is an important clue", dropping the word "that". Can we drop che in Italian?

No, you cannot drop che in Italian. While English allows you to leave out "that" in sentences like "I think [that] this is...", Italian strictly requires che to connect the main clause (Penso) to the second part of the sentence (questo sia...).

If the sentence were about multiple clues, how would sia un indizio importante change?

It would become siano indizi importanti. Sia changes to the "they" form of the subjunctive, siano. Indizio is a masculine noun ending in -io; to make it plural, you just drop the final -o, leaving indizi (not indizii). Finally, the adjective importante changes to its plural form, importanti.

Indizio is masculine, so why doesn't the adjective end in -o (like importanto)?