[RPG] How many people can fit inside Mordenkainen’s Magnificent Mansion

The short answer is "Your player is definitely running some sort of con job on you". But here's the specifics for Revised 3rd, with some background from the other editions.

Restaurant: The salient points read as follows.

The atmosphere is clean, fresh, and warm. You can create any floor plan you desire to limit of the spell's effects. [Up to three 10ft-cubes/level]

By the RAW you could certainly create a restaurant "atmosphere" in the mansion. Though a savvy GM might require the wizard to produce an actual blueprint (or understand someone else's) first to do something so specific. After all, not every PC is an architect.

The place is furnished and contains sufficient food-stuffs to serve a nine-course banquet to a dozen people per caster level.

At the minimum caster level of 13, he could produce enough food to serve 156 people a quite impressive meal. And although the Focus cost of the spell is 15gp, the cost of a banquet per person is 10gp. That means that, if the caster can find an average of 6 people an hour willing to pay 10gp per person for the meal (a big if), the first use would net the caster a healthy 1545gp profit with a steady income of 1560gp per casting thereafter. On the other hand, the same spell cast at the same level by an NPC has a cost of 925gp.

There are likely some ways to dissuade this behavior (if you want to), including making it a full-time job for the PC. After all, a 13th level party earns roughly 13,000 gp per encounter. Even split 6 ways, that's a lot more money in a lot less time. But really, such a thing deserves a question in it's own right.

However, it should be noted that the developers of other editions were well aware of the bugs in the spell that the developers of 3rd edition either decided to ignore or thought of as a "feature". In 2nd edition, any food the players eat loses it's effects as soon as they leave so at 10gp a plate you can bet he'd have some pretty upset customers. In 4th, the food is no longer illusory, however the "mansion" only has enough room and food for 50 people, period. Any (presumably uneaten) food disappears if removed from the mansion, nor does it contain qualifiers that indicate the food to be anything other than "satisfying".

A staff of near-transparent servants (as many as two per caster level), liveried and obedient, wait upon all who enter. The servants function as unseen servant spells except that they are visible and can go anywhere in the mansion.

Emphasis mine, obviously. The spell rather clearly defines where the unseen servants are allowed to operate and thus by exclusion, where they are not. The unseen servant spell specifies that "if you attempt to send it beyond the spell's range [which, being produced as part of the mansion spell, is presumably the mansion], the servant ceases to exist." In addition, the servants wait upon all who enter, not just the caster which, as I read it, means they wouldn't be particularly suited for most of the tasks a restaurant requires. In fact, the unseen servant spell contains a whole host of other restrictions that are probably well worth your looking up.

Fast Travel Network:

You can cast as many Mansion spells as you have spell slots for each day, however Mordenkainen's Magnificent Mansion is temporary, meaning if this could work it would be very short-lived. Specifically, each mansion lasts only 2 hours per level.

Each spell creates an extradimensional space. D&D is riddled with extradimensional spaces (rope trick, portable hole) and none of them are inherently connected. Trying to use this as a fast travel network would be rather like saying you put your MacGuffin into one Bag of Holding and pull it out of another.

The spell entry itself actually has a great deal to say on the matter as well. Again, emphasis mine.

an extradimensional dwelling that has a single entrance [....] The entry point [....] the portal [....] the entrance [....] the place can be entered only through its special portal

I'm pretty sure there's no ambiguity there to wiggle through.

I'm sorry to say that its seems that you gave your players an amount of freedom that most of us could only dream of getting, but this particular player has decided to abuse the privilege. Worse, he's attempted to cover for it by trying to keep you misinformed on the actual nature of the rules. I suppose if one were being generous they could assume that the player misunderstood, but they certainly bear close watching in the future.

Short answer, they would be expelled too, unless you give the order to preserve it to one of the servant but the item will be lost forever.

Long answer:

Is the same mansion? No.

PHB 261:

You conjure an extradimensional dwelling in range that lasts for the duration.

As you can read it does not say you conjure a new or an existing mansion. Later on in the same description, it state that you can create but it does tell you anything about reusing the existing one. It also does not stop you to recreate an old one, but is not going to be the same one. Furthermore, at any point on the description says something about the servants remembering you, reinforcing the idea that is a totally new one.

You can create any floor plan you like

What happen to the item left?

Following the same logic, the spell description also state what the servant can do, under their limits. And since you can give things to humans, it is safe to assume that you can give to them items. You can order to keep the item, but as stated earlier the item will be lost.

Each servant can perform any task a normal human servant could perform, but they can’t attack or take any action that would directly harm another creature.

Now, what would happen to items that you leave in the mansion? The "mansion" does not hold ownership on any item that you have or leave behind. The same way you do not own any items in the mansion (you cannot take them out). So, unless you "give" to the mansion the ownership of an item, it would behave as if the Object is a Creature and drop it.

The servants can go anywhere in the mansion but can’t leave it. Furnishings and other objects created by this spell dissipate into smoke if removed from the mansion.

When the spell ends, any creatures inside the extradimensional space are expelled into the open spaces nearest to the entrance.

We can expand the ownership logic further. The nourishment of the food given by the spell does not disappear at the end of the spell or when you leave the mansion, but the furniture do. This mean that in order to take things out of the mansion they have to be given. This logic can be applied to your own stuffs. The "mansion" does not have any ownership of your stuff, hence, they are expelled from the mansion when the spell end (given that you did not give them to a servant).

It contains sufficient food to server a nine-course banquet for up to 100 people

Now, you might want to say: a creature is not an object. And it is true, but it is more of a mechanical way to delimit and categorize elements in the game. That would be a total debate but as far as your question goes is not that relevant. Furthermore, your DM is the one that has the last word, if you are the DM pick what would be more sensible for you.