Silent Image allows you to create a 15ft cube which is the equivalent of a huge creature.
If PC's create the image of an adult Dragon for instance, their rationale is that anyone fighting them would think twice with an adult Dragon in the area. Wouldn't they just flee?
There are no rules saying that a fear check is required, but from a common sense angle, I wouldn't hang around to physically interact with it (or wait for it to physically interact with me!!?!) to find out if it's an illusion or not... and sure, there aren't any other sensory effects other than visual, but still, I wouldn't hang about.
One DM I was under allowed the spellcaster to roll spell check (prof+spell modifier) to substitute an intimidate or deception check for the image. The higher the roll, the more realistic and/or terrifying the creation. It was a happy medium that both the player and the DM agreed upon.
Depends on how intelligent the enemy is and what rules the DM uses for identifying spells. Most creature's immediate response is going to be to run away, but when they don't hear/feel the dragon chasing them, the intelligent ones will realize something's wrong. Those with spellcasting knowledge may realize that a spell that really produces a dragon would be very high level, and the DM might also allow them to try to identify the spell as you cast it.
The Table of Contents from XGtE suggests it'll include rules for identifying spells, but I suspect most DMs already have some house rule for this since otherwise counterspell is kind of impractical.
In my opinion, it depends a lot on how well-designed the illusion is.
If a dragon appears in front of you, that's an immediate save (possibly with advantage in case of intelligent opponents - sure, the dragon may have just materialized, but come on).
A dragon in a large room with no entrance that it would fit through? Average-intelligence creatures will think something's fishy.
A dragon outside his usual environment? Intelligent creatures may pause to consider (at a safe distance). Goblins will stop running when they run out of lung.
You've been hearing about a dragon in the area from NPCs? Dragon claw marks on the stone? A half-eaten bull hanging from a tall chain? A curiously acidic smell in the air as you approach the large cavern? Then a dragon resting on a top of a small pile of treasure, with corpses littered about? Run. Although the giggling fit of the Illusionist may provoke a save regardless.