As you can see from the wide range of responses, there are a lot of possible ways to do this, depending on what effect you want the power to have.
The Illusion effect by itself only affects Perception, manipulating how things appear. Anything else requires another effect, and since all effects require descriptors that describe how they appear, you may not need the illusion effect at all unless you want to mess with perception. As Dr. D points out, anything that has real effects like Damage or Summon or Move Object doesn't necessarily need the Illusion effect
Using your examples, whipping up a gun "illusion" that works like a gun would be a Ranged Damage effect. It could shoot and damage like a gun, but you can say it never runs out of ammo and can't be disarmed or broken (the normal limits and complication of a real gun). Mechanically, this is identical to shooting beams out of your eyes, it just looks like a gun in action (different descriptors). Making fire would be Damage with different modifiers and descriptors on it.
Summoning a creature can be the Summon effect, but you can often make it out of something else if you only want your summoned creature to do a few things, or more precisely, have few effects. A "real" summon can work independently and be attacked and killed (unless you modify it a lot, which I find can be unnecessarily cheesy), or you could have a Move Object effect with Damaging that looks exactly like a creature which can attack and move heavy stuff as if it had Strength equal to MO rank but (like the gun above) can't be targeted for damage, although you essentially have to work it like a puppet from a distance.
Now the Illusion effect can still be used with these powers, depending on how you want it to work. The basic descriptor for each power would make them look like guns and monsters, but deceiving opponents into believing they are real is another matter, otherwise you basically have something like the Green Lantern ring which can make stuff that effects the world but has an obvious source. Linking Illusion to the effects would make it more difficult for opponents to disbelieve, so instead of attacks simply going through the creature or gun and giving away the trick, the Illusion responds logically (creature seems to bleeds but doesn't slow down, gun seems to shift away from disarm attack) so the opponent may be fooled into wasting effort on treating the illusions as real.
The trick is making the effects look like they come from the illusions, but even if opponents see through that, the effects still happen. Saltcrow's array above would give you all of that (although you'd have to add in the Move Object), allowing for real effect with a coat of Illusion paint, so to speak.
Greyman and King Snarf's suggestions sort of work in the opposite direction, where the opponent has to believe in the power (ie fail resistance by Will or Insight) for it to work. This can be purely psychological or a particular style of magic or something else, depending on your game. These powers can be cheaper, since they are Flawed, but as Dr. D points out, they shouldn't have any effect on inanimate objects that don't have minds.
It really depends on how you and your player want it to work (and not work), so be specific. I'm no mind-reader, but I suspect they want the real effects with a dash of Illusion. I also suspect they don't want to Create stuff, just get the effects that stuff would make, so this would be my suggestion for a build:
Mirage Master: 50-points array, all dynamic- [53pp]
•True Illusion: Illusion 10 (all senses)
•Real Effects: Perception-ranged Damaging Move Object 12, variable descriptor 2 (anything created by illusion)
Similar to Saltcrow's, it's a relative simple and very powerful Dynamic array. Because it's Dynamic, the more powerful you make the effects, the less deceptive the Illusion can be. For instance, you could evoke a tank illusion that shoots with the power of a tank (Damage 10), but once engaged it can be seen through it with a DC11 Insight check. Whipping up a heavy pistol (Damage 4) would have opponents believe it's real unless they make a DC16 Insight check. The damage still works if it hits, though.