[RPG] When do you no longer need to sleep

Your predicament is a pretty common one, and applies to any GM who has a player focused on summoning monsters. Even without the brokenness that is Master Summoner, summoning-focused characters can quickly break the action economy and make it so the rest of the group has little to do, most of the time. That said, here are a few things that you can do to reduce the power of your Master Summoner player without removing his flavour. There are basically two things to do here: carefully limit the creatures that Summon Monster is capable of summoning, and make the Master Summoner's resources matter more.

Don't add monsters to the Summon Monster list without careful consideration

The list of monsters that you can summon with Summon Monster is reasonably well-balanced as it is. However, there are a bunch of unstated assumptions that it has that can cause some serious problems if they aren't adhered to. Some of your problems come from this.

1. Ban Summon Good Monster

   That feat is really super powerful, especially at lower levels. It gives you way more battlefield control options than you would normally get, as you have already noted. Most of the monsters on that list are fine, but no one is going to summon the well-balanced monsters off a list like that, they're going to summon the awesome, way-too-powerful ones. If you don't want to ban this list outright, then at least go through it with a fine-tooth comb and assure that the abilities that you get from it at a particular level aren't out of line with what you get from the normal list. For example, the first creatures that have any abilities that are either ranged or spells are in the Summon Monster 3 list, and those creatures are pretty terrible is a stand up fight (Dretch and Lantern Archon).

2. Ban non-standard Elementals

   This is similar to the point above. When Summon Monster was first written, there were 4 elementals: Fire, Water, Earth, Air. Each of them is an effective tank in their environment, and are reasonably well-balanced. Allowing the player to summon the other 8 types of elementals that have been added since is adding to his versatility by a significant amount, and versatility equals power. As you've noted, some of the additional elementals have abilities out of line with what the normal elementals have. You don't have to allow the player to summon more powerful monsters (like the Mud Elemental) if it's going to mess up your game.

3. Keep the general Summon Monster guidelines in mind when adding new monsters

   To sort of go back on what I said above, there's nothing wrong with letting your player have more or different creatures to summon, as long as you're careful about what these new creatures give the player at that level. Make sure you look carefully at what a particular level of Summon Monster gives you before adding new things to that level. For example, with Summon Monster 2, you have the following roles: melee ground tank (most of them), flying tank (air elemental), swimming tank (water elemental, octopus, squid), high damage/poison tank (fire elemental, giant centipede, giant spider). The only battlefield control options available to any of these creatures are the normal combat maneuvers, mainly grapple and trip. None of them have more powerful control options like the faun or mud elemental do. This extends through most of the levels of Summon Monster. For example, nothing below Summon Monster 9 has the ability to cast spells like a PC.

The final arbiter of what the player is allowed to summon or not is you, as the GM. If you think that a particular form is out of line for the power that a level of Summon Monster gives, then you are well within your rights to ban that form, or put it on a different level of Summon Monster. It doesn't matter if the rules say that the player can summon a particular monster; if using a particular summon is going to make the game less fun, then that summon should be banned, or otherwise limited.

Make the Master Summoner's resources matter.

The standard game rules make some assumptions about the kind of game that you're playing, and tune player resources based on these assumptions. The game assumes that the average player is going to have 4 encounters in an average day. For a Master Summoner with 18 Charisma, that means that they can summon 2 monsters in each encounter, and 3 in one of them. Adding 2 monsters to a fight is something that can be worked around, in general. If you have significantly fewer encounters, then you need to figure out a way to make your player's resources matter again.

1. Intelligent enemies should have intelligent protections.

   For example: Any intelligent enemy that knows about the summoner is going to have a Protection from Good ready to go (whether from a potion, and item, a scroll, or a spell prepared, depending on the enemy). Protection from Good doesn't shut down your player entirely, but it does make it so he needs to use more of his Summon Monster abilities in a single combat to remain effective. Spellcasters can use Dispel Magic to quickly end a summon. More prepared enemies can use Magic Circle instead of Protection, which is a little more effective.

2. Reduce the number of summoned monsters at once.

   Like you say at the end of your question, you might consider limiting the number of monsters summoned to two spells. The player could use one eidolon and one Summon Monster spell, or two Summon Monster spells, but no more. This means that the player can basically use the same number of Summon Monster spells that he could normally use per encounter in a 4-encounter-per-day game. You might allow the player to use extra uses of the ability to get more monsters at a time, to make the player feel like those extra uses are still useful. For example, maybe the first 2 castings take one use each, but any after that take 3 each.

3. Reduce the number of uses per day.

   If your campaign requires only one or two encounters per day, then it might be helpful to reduce the number of Summon Monster uses that your player gets directly. In a 2 encounter per day game, reducing the number of uses to 5 or 6 would likely be helpful. This might make your player feel shafted, so it might not be the best thing to do.

4. Use more numerous monsters, or ranged monsters.

   Basically, alter your encounter design to take the summoner into account. If there are a dozen orcs charging in that will likely overwhelm the party, the summoner can deal with them while the party deals with the rest of the encounter. Alternately, powerful ranged monsters can target your summoner, making it a priority for the summoner to send minions to deal with that threat while the other players take out the main encounter.

The Mummification discovery says:

he becomes immune to cold, nonlethal damage, paralysis, and sleep.

Cit. d20pfsrd.com

This is a list of things that the character is immune to. "Sleep" means the sleep spell, not that the character lacks a biological need to sleep.

Note that although d20pfsrd.com links to the sleep spell in their wiki, not everyone does. This is an interpretation of the discovery's text. However, sleep is not a status condition or damage type, unlike the other entries in the discovery's text.

Compare mummification's text to something like the Construct description:

Constructs do not breathe, eat, or sleep. Cit.: d20pfsrd.com

The ability specifically mentions not needing sleep. Mummification's text does not.