From a very legalistic reading of the rules, you can use assassinate only once per encounter. Using it requires the opponents be surprised; they are only unaware of their opponents once in a fight; and stealth doesn't grant surprise status.

In effect, think of it like this: a surprised opponent is one that is entirely unprepared for being in a fight right this instant. When you attack an unsurprised opponent from hiding, they are already expecting attacks, so they are less vulnerable then when surprised but more vulnerable than when they can see you specifically.

It might actually be more and less complicated than that

However, that is a fairly conservative legalistic reading. It requires reading the description of surprise as ungenerously as possible—which, in general, is the safest way to read a rule when you're a player. Better to be right that you don't get goodies, than expect goodies and be wrong, yes?

That said, D&D Next is going to be weird for any player from the last decade and a half of D&D editions, because it has the explicit goal of reclaiming the heritage of AD&D and earlier editions that 3e left behind. And a major part of that heritage (for good or ill) is those editions' interpretability. Unlike 4e and (mostly) 3.x, the rules were only hard-and-fast where the rules were unambiguous, and where they were ambiguous the DM was expected to decide what worked best for their home game. When something was unclear in the rules, sometimes there was an official answer, but as often there wasn't.

This was considered a feature by the designers, especially in the original edition of D&D and in the Basic line. This was slightly less the case in AD&D because it was also meant to be the "tournament edition" of the game, but it never shook that heritage and it has interpretability very deeply ingrained into its structure and how the rules are explained.

Arguably, 3e didn't shake that heritage completely either. 3.5e got closer, but still has a few lacunae that drive people to distraction. 4e was the attempt to refine it to perfection and eliminate even the possibility of lacunae... and WotC didn't like the customer rebellion that edition caused. Hence Next, and why it is going "backwards" in many ways.

It's debatable whether Next is going "backwards" in regards to interpretability specifically, but as I hope I've shown, it's a distinct possibility that the rules for surprise and stealth are every-so-slightly unclear on purpose.

So what?

Well, so what? If the rules are unclear, then making the most conservative, power-limiting interpretation is correct, right?

Power problems might not actually be problems

Well, no, not exactly. Next is designed to have a much flatter power curve than any prior edition from Wizards of the Coast. A neat thing about a flattened power curve is that it makes the "sweet spot" of most-enjoyable levels much wider, which is a large part of why they wanted it. But also, as anyone can tell you who has experience with non-WotC D&D editions, a very flat power curve also means that character power is less variable and, often, a more-powerful character doesn't have the ability to travel far enough "upslope" on the power curve from the rest of the group; if the power curve is flat enough, or the character's advantage is unoptimal enough, they simply don't cross the threshold of problematic power difference.

So that's a neat feature. It was taken for granted by AD&D DMs and players, and it gave those groups much more flexibility and power to create interesting adventures and mixes of PCs without running into balance problems or putting constraints on story and adventure design. It was only in the 3e era that "power disparity" entered the lexicon of D&D players.

With Next's flatter power curve, it's entirely possible that power disparity problems are only in our habits learned from 3/4e, and aren't applicable to Next.

Surprise and stealth

So if Next doesn't have the kind of power-imbalance problems that we're used to having to squash, our habit of reading the rules as conservatively as possible may not apply. It wasn't necessary in pre-3e D&Ds, and maybe it won't be necessary with Next.

And if interpretability is a deliberate design feature of Next, then there may actually not be an official answer.

Combine these two possibilities, and you have an interesting result: it might not matter which way you read this rule. And if it might not matter, then different DMs might run this differently in their games, with some allowing Stealth to be used to hide your presence, and that counting for triggering "presence" condition necessary for surprise and assassination criticals.

This is often how AD&D DMs ran thieves' backstab ability. Given how much Next is attempting to recapitulate AD&D and earlier editions, and given how these rules around surprise and stealth look suspiciously similar to those earlier editions' rules for surprise and stealth, and given how the power curve of Next has been brought back into line with the power curves of AD&D and BD&D... I would not be surprised at all if the answer to this question was: Ask your DM.

You are right for the number of critical hits. The Assassinate feature (PHB, p. 97) says:

Starting at 3rd level, you are at your deadliest when you get the drop on your enemies. You have advantage on attack rolls against any creature that hasn’t taken a turn in the combat yet. In addition, any hit you score against a creature that is surprised is a critical hit.

When an enemy is surprised, you play your full turn. If you multiclass into fighter to have Extra Attack, yes, you can have more critical hits if you hit (you have advantage on your attacks since they didn't move yet). One detail that you must not forget is that the Sneak Attack damage is applicable only once in your turn:

Once per turn, you can deal extra 1d6 damage to one creature you hit with an attack

With a level 5 fighter and a level 3 rogue with two daggers, the damage would be (assuming they all hit):

2d4+DEX (first hit) + 2d4+DEX (second hit) + 4d6 (sneak attack damage) + 2d4 (off-hand attack)