How can Blackcoin get 1st confirmation in 10 seconds? According to it's official page, Blackcoin used scrypt as its Proof-of-Work during the phase of initial coins' creation. But now it's purely Proof-of-Stake, and they claim to have a speed of just 10 seconds for first confirmation (and only needing 10 confirmations to get an almost guaranteed transaction).


How does their pure PoS model serve to verify transactions, without the risk of double spends?
How can they create blocks as often as 10 seconds without having massive amounts of orphans?
Blackcoin is a fork of Novacoin which is a fork of Peercoin which is a fork of Bitcoin.
In your own answer on how PoS mining functions is the answer to this question:

For Peercoin specifically, PoW and PoS blocks are independent. Just as you're betting your consumed electricity and CPU-time vs. the possible PoW-blok's reward, in the PoS blocks you're betting your coin-age: the amount oF PPC you own multiplied by the number of days they've sitted idly at your wallet. It must be a minimum of 30 and a maximum of 90 days for your coins to start generating tickets for the PoS raffle.
Should your ticket win, you earn 1% interest and lose all your coin-age, so your coins are, from the network POV, as though you had just received them. I.e. you'll need to wait another 30 days for them to be able to pay you interest again. Over time, though, you're just supposed to earn about 1% annually.

Honest nodes will only attempt to generate blocks if their stake is below the limit.  This cuts down on traffic immensely.  Looking out for violators cuts down on DoS as well which has only strangely been recently implemented in some coins.
I could find no major deviations from NovaCoin except for a decreased block spacing which may or may not apply to the PoS portion, faster coin maturity, and a few additions to net.cpp communications.
I have found no posts complaining about orphan blocks or any remarking that there are few except for this question.
I have found a few posts claiming that PoS will create extra traffic but nothing to substantiate it.
In short, BlackCoin appears to be the PoS Fastcoin, and throttled PoS will produce no more bandwidth consumption than PoW.
Throttling mechanisms
NXT
NXT is much more controlled than the other PoS coins:

What does this transparency mean? It means that anyone can predict (with very high probability) who and when will generate next block(s). And this gives us superior advantages:

Transactions can be sent directly to the miner who will mine the next block (if he decides to reveal his location on the Internet), thus saving traffic and coming much closer to VISA/MasterCard processing volumes.
Blocks can be generated in advance and sent to most of the miners before they become valid (timestamp validation), thus greatly reducing rate of orphaned blocks.
Due to ability to predict timestamps of future blocks (rate of blocks) it becomes possible to set appropriate fees to assure quick confirmations for important transactions (without paying too much for inclusion into a block).


NovaCoin
This will seem more familiar:

Novacoin uses the mixed Coin-Age/CoinDayWeight approach to provide proofs of the stake. The proof-of-stake difficulty is adjusted so as to limit the rate at which new blocks can be generated by the network to 10 minutes target spacing rate. Due to the very low probability of successful proof generation, this makes it unpredictable which computer in the network will be able to generate the next solution.
It's performed through scanning all available inputs in order to find lucky one that satisfies following condition:
SHA256(SHA256(KERNEL)) &lt; CoinDayWeight *  NetworkTarget
Miner has to find a SHA256 hash that is under the target value.

In NovaCoin's case, it's still a little PoWish, but traffic is cut down because those who cannot mine because of insufficient stake either don't or are blacklisted for violating the rules.
Once a node has a conforming block, it stops working on that block index and moves to the next.  Eventually, no one is left working on the wrong chain.
BlackCoin
Based upon the above inspection of the code which is a fork of NovaCoin, BlackCoin works in an almost identical way except the spacing is tuned way down, and there are a few network enhancements to make the network a little stricter.
As a side note, based upon bitinfocharts's calculations, the 10 second advertisement is never met on average and is more like a lower bound; however, the intended spacing is one minute, so either the spacing formula is wrong, or PoS is actually so performant that it has busted the formula.
Ophan management
NXT is the extreme case.  My guess is that it rarely has any orphan blocks because the subsequent miner is selected, so an orphan is generated from a network malfunction rather than by design.
NovaCoin's first line of defense is PoS which limits the number of potential miners.  Since the longest conforming chain is accepted just as with PoW, hashpower dedicated to a losing chain is reduced for each now block index.