I'll answer your questions and respond to what appear to be some misconceptions you have.

Surprise attacks

Here's how I imagine the conflict: The darkmantle attacks an unsuspecting PC. Since the PC is surprised, they only offer passive opposition. The attack is likely to succeed. Instead of dealing damage, the darkmantle wraps around the PC's head, creating the blinded aspect. If the darkmantle succeeds with style, it wraps itself around the PC so well, that the PC cannot breathe.

Your target might be caught by surprise, but that's purely a story detail. If you have nothing to invoke, surprising them won't necessarily have any influence on your roll. Fate Core doesn't have anything like, say, D&D's mechanic of being caught flat-footed.

If you want to surprise someone and get a bonus to some action for it, you'll have to work for it somehow:

• Create an Advantage and place an aspect on yourself like Well Hidden. As a Darkmantle, you might even have a stunt to that lets you place a stealth-themed aspect on yourself for free! Then you're hidden, and you can invoke that when you take the enemy by surprise.

• Invoke your Darkmantle high concept, and get a bonus for being such a sneaky attacker. Remember that you can use Create an Advantage to place free invocations on any of your existing aspects - including this one.

As a Darkmantle, you could further improve this with a stunt like one of the following:

Death's Approach. Gain a +2 bonus to any attack using Fight, whenever you're hidden from your target. ("Attack" here refers exclusively to the attack action; see Fate Core p90)

Backstab. You can use Stealth to make physical attacks, provided your target isn't already aware of your presence. (This one's actually from the book! Page 89)

Self-Compelling to attack whoever's attacking you

Can the PC being blinded/suffocated use their own blinded or cannot breathe aspect for a self-compel? Something like:

I wanted to defend against that other enemy, but now that I'm blinded / cannot breathe, I have to take care of the darkmantle first

No - unless there's more to it than that.

In a straightforward fight with some enemies, focusing on the person attacking you instead of someone else doesn't really complicate your life or introduce any drama. That alone doesn't make for a good compel.

Compels are supposed to make someone's life complicated and introduce unexpected drama - they're introduced this way on Fate Core page 14. Their examples include failure at a goal, someone's choices being restricted, or unintended consequences springing from an action. Their gameplay example features someone having poor manners at a very important diplomatic occasion. Compels exist to encourage players to accept hardship and failure where it would be positive for the story, because they still get something out of it.

Let's make this more dramatic.

You're the PC being suffocated by a Darkmantle. You still must pursue the Six Fingered Man who's escaping (The Six Fingered Man Killed My Father), or you absolutely need to reach that lever and save the others (My Crew Is My Family).

This is a situation with dramatic tension, and either way works for a good self-compel. You could self-compel to pursue your goal, struggling despite the fact you're being strangled, or you could self-compel to deal with the person strangling you first - meanwhile risking letting the Six Fingered Man escape or putting your crew in harm's way.

Can an aspect deal damage?

Being unable to breathe should make you suffer some consequences, eventually, no?

Well, yes and no. Yes because you can create aspects like On Fire which hurt the character in question. But...

Fate Core has no concept of hit points or damage.

Consequences and stress are not hit points or health. They're a very different beast. Think of them as your staying power in a conflict. The more Stress you can take, the more you can shrug off or handle before you have to start taking Consequences and attacks begin to really affect you. Stress and Consequences together are a measure of how much you can handle before you are Taken Out or need to surrender.

So the NPC in question might be genuinely being suffocated. Likewise, someone with an Acid Burns aspect on themselves (however they got it) is genuinely hurting - but they're not taking damage, because damage doesn't exist.

Then how do you take out a guy you're suffocating?

Use the Attack action! Use it to suffocate him, and burn through your free invocations to hit harder give them more stress to soak up. Alternately, compel them to concede the fight instead.

The Cannot Breathe aspect alone does nothing more than make something true. He won't get taken out. If he's still hanging in there after ten turns, you must just be really lousy at suffocating people - he's clearly managed to get a breath in here and there.

Because of this, it makes more sense to pick an aspect like Suffocated by a Darkmantle.

Passing Free Invocations

Do opponents of the PC have to be allies to pass a free invocation of the blinded aspects among themselves?

You can pass free invocations to anyone. Fate Core p70 has this to say about Free Invocations, in a paragraph on the bottom left:

If you want, you can pass your free invocation to another character. That allows you to get some teamwork going between you and a buddy. This is really useful in a conflict if you want to set someone up for a big blow—have everyone create an advantage and pass their free invocations onto one person, then that person stacks all of them up at once for a huge bonus.

You can pass free invocations to someone you'd consider an enemy. (Who knows, maybe you want to save them from someone else's killing blow so you can get information out of them first, or something.)

Can you create two aspects?

You can create as many aspects as you want, but there's no provision for creating two at once in the same action. This would usually take a rule-breaking stunt that adds aspects. For example, Atomic Robo RPG has a stunt called Little Black Book: when you create an advantage with contacts, you can trade off each free invocation you might otherwise get to create a new aspect instead, meaning you'd get up to three total aspects (but no free invocations) when succeeding with style.

If your fellow players are happy to introduce some new mechanics, you could borrow the Overflow mechanic from Dresden Files: BESW describes it here. This would let you take the excess margin by which you succeeded at an action and perform one extra action, given it meets certain conditions. Both could be Create Advantage actions, letting you place two aspects at once.