If you're looking for RAW, then we should start with the Maximize Spell metamagic feat itself, from the PHB:
All variable, numeric effects of a spell modified by this
feat are maximized. A maximized spell deals maximum damage,
cures the maximum number of hit points, affects the maximum
number of targets, etc., as appropriate.
Saving throws and opposed
rolls (such as the one you make when you cast dispel magic) are not
affected, nor are spells without random variables.
That seems straightforward enough: If it's a variable in the spell itself, you can maximize it. If there are no random variables in the spell itself, you can't. It's also heavily implied by the bit about saving throws and opposed rolls that only the rolls in the spell itself are affected, not rolls caused by the spell itself.
Let's see if applying this reasoning to your examples helps. We'll start easy and work our way up to the important ones.
Fabricate: Conjures a set amount of material per level. You couldn't Maximize this spell if you wanted to, there's nothing to maximize.
Summon Monster: Your DM is correct in saying the Maximized version maximizes the number of monsters (a variable in most versions of the spell), not their damage- the spell doesn't affect their damage, and so can't Maximize it.
Claws of the Beast: I believe this is actually a psychic power, but pretending for a moment it's a 1st level spell, yes, you would maximize the damage caused by the claws. Spending a spell slot three levels higher is reasonable in exchange for changing your damage from 1d4 to 4 per attack, and it is a variable listed in the spell itself.
Now for the spells with effects. I won't list a great number of examples, but hopefully it will be enough to give you an idea of how it works in general.
Acid Splash: The damage variable is listed in the spell itself and gets Maximized. Given that you've spent a 3rd level spell slot to deal 3 damage, this is far from an absurd use.
Blade Barrier: An example of a spell you would actually want to maximize. Sacrificing a 9th level spell slot to deal 90 points of damage at a whack is a pretty good deal, but remember that the same cleric casting it as a 6th level spell would deal 50-ish points anyway.
Cloudkill: Those who fail their saves (and don't die instantly) would indeed take 4 Con damage per round. This is from an 8th level spell, mind.
Disintegrate: Maximize was designed for spells just like this and Fireball. The ray deals maximum damage in exchange for a 9th level slot- take that, blade barrier.
Dragon Breath: Though it is described as something that "mimics" dragon's breath, the effect of the spell is ultimately that you can make a cone or line of one kind of elemental energy. Depending on the combination, you deal a certain number of dice of damage and grant a set kind of save. If the spell had instead said that you gain the breath weapon of a specific kind and age of dragon, with no mention of how much damage that breath weapon does, you couldn't Maximize it... but it gives you variables, and Maximize spell specifically maximizes those variables.
When it comes right down to it, RAW states that Maximize Spell affects all of the spell's variables. If the variables are not intrinsic to the spell, they aren't listed, just as fabricate doesn't list the damage caused by a sword because that isn't intrinsic to the spell. If the variables are intrinsic to the spell, they are affected by Maximize Spell. While this might seem OP at times, always remember that you're giving up a much more powerful spell, one three levels higher, in exchange for not having to roll damage. Most times it will be a fair trade.