There's no need to house rule this — you just need to start enforcing its restrictions. Allow me to draw your attention to its area of effect:

4 square″ + 1″ square/level

(Aside, this is taken from PHB page 95, since the Illusionist version of the spell has different range and area of effect.)

These are table inches, which we could convert to feet/yards, but the following will be simpler if we just compare table inches directly with fireball's numbers.

A fireball has a radius of 2″. Let us ask then, “what level would an illusionist have to be to cast a phantasmal force large enough to contain a 2″ radius sphere?” Let's make a first-order approximation using the minimum number of 1″ squares necessary to create an area in which the image of the sphere could appear. The area of effect of fireball is three-dimensional, but the area of effect of phantasmal force is two-dimensional, which presents an odd issue. However, phantasmal force is described as being able to create images “within the boundaries”, so let's be as generous as the spell seems to be intended, and say that the vertical space it can create the illusion within is “good enough” for our purposes and we just need the footprint of the illusory fireball to fit inside the phantasmal force's area of effect.

We'll assume as a first-order approximation that each 1 square″ of area of effect can't be divided, so they have to be tiled as whole square table inches. Inscribing a 4-unit sphere's footprint (a circle) inside a pixelized shape requires a 4×4 square of squares, or 16 tiled squares.

So, as a first approximation, an illusionist needs to have 16 square table-inches of area of effect to play with to be able to make a phantasm of a full fireball. That requires being level 12 to pull off.

But maybe you think tiled squares aren't generous enough. Let's allow the table-inch squares of area of effect of the phantasmal force to be subdivided infinitesimally so that the area can be a cylinder that just barely contains the footprint of an illusory fireball and see where that gets us. (Some DMs might reject this move since the area of effect is given in squares and they may require a straight-edged area of effect, but some others might allow it with the reasoning that it's fine as long as the final area matches regardless of shape.)

A 2-unit-radius sphere has an area through its widest point of just over 12½ units, rounding up to 13 square″ required. So even being super-generous, it would still take an illusionist of level 9 to use phantasmal force to create an illusory fireball.

Clearly, creating illusions of fireballs with phantasmal force isn't something that your players should be doing at first level, or even 5th level when their magic-user friends are starting to throw real fireballs.

Conclusion: You don't need to house rule, just give the players a reality check

So, there you have it: you don't need to house rule this at all, you just need to pay proper attention to the relatively small area of effect, and break the news to your players that you've been accidentally letting them create a 9^th-level illusionist's phantasmal forces before they were actually 9th level, and won't be doing that any longer.

If they are 9th- or 12th-level, then this isn't overpowered at all, because they have access to equally (or more) powerful effects already and cleverly using their resources like this should be letting them paste low-HD enemies by the truckload. So again, there simply isn't a problem if the area of effect is enforced.

Addendum: Don't overlook the audio limitation either

The above is all completely ignoring the impact of the stipulation that a phantasmal force is silent. Is a fireball silent? Not at all. An illusory fireball with no sound effects is not very convincing, and unlikely to fool even stupid opponents, even stupid opponents who have already been hit by a real fireball. In fact, having just experience a real one with all the sound and fury of real fire, they'd be more likely to notice that a silent one is not quite right.

Addressing your concerns in order:

Spell located in PHB pg.276

Passive, in combat

The only way to check it in combat passively is to pass something through it. Silent Image does not resist this as the wording of the spell states:

Physical interaction with the image reveals it to be an illusion, because things can pass through it.

However, in combat a creature doesn't naturally assume something is an illusion and attempt to wave a hand through it or run into it's space. This is why it requires an active check, which will be covered later.

Passive, out of combat

If you try to step on an apparently real bridge and tumble through, you would passively know that it was an illusion. This is covered much the same as above, in combat.

Active, in combat

This is the way the spell is actually worded. Specifically:

A creature that uses its action to examine the image can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC.

This means that they have to use active checks in order to discern the image is an illusion if they're in combat. The reasoning behind this would be simple logic. If you were engaged in combat and an Earth Elemental suddenly rose from the ground, how certain are you that it's an illusion and not a spell? What are the consequences for being completely wrong if you tried to just ignore it and move into it's space? An active check is based on somebody thinking it's not real, and then testing it to make sure, but testing it relatively safely.

Consider that testing it may include prodding it with a sword or tossing a rock through it to check to see if it has substance. Basically, something that requires an action to attack, follow through, and wait to see the result. It's not a bad use of an action as it effectively defeats a hazard in a mere 6 seconds (so long as you pass the DC check!)

Active, out of combat

These are your typical take 20 scenarios. Any active check out of combat is something players can simply repeat over and over to ensure that what they're looking at is very likely to be real. However since the spell states that physical interaction reveals the illusion for Silent Image, the basics of an active investigation should be touching it with something, which would reveal it's nature.

Lastly:

You are correct: Any physical interaction sees through Silent Image. Be careful if utilizing this knowledge in game (meta-gaming) because as a DM I would start mixing in invisible creatures suddenly popping up and giving them opportunity attacks if you try to casually interact with them physically in the middle of combat. Reaching out to see if that Drow Warrior is really real is a great way to lose a hand or arm.