1. The table is in alphabetical order, and, in general, the question which service is the best and was opened earlier is highly controversial.
even better 
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2. At first glance, it seems so. However, I would like someone to share a real experience with concrete examples. The devil is in the details, as you know. After registration some sites may require the scans of documents or check the phone number. Some of them can do something similar when smb withdraws their money. Others may delay the payment for a long time. And it does not suit to us. In addition, I would say just the opposite - the less legitimate site is the more suitable for the mix it is, I mean that there are low chances that site will share logs or has logs at all. i.e the less the site is legitimate, the more it will be similar to the site of the first group.
- all sites (services) keep logs such as your IP addresses, your deposits, withdrawals (the transaction IDs) because they use them for many purposes like for example if you wanted to recover your account if you lose your password.
- using these services to mix coins means you only want "public" to not know about your other addresses but the site you use and in case the law can find out about it easily.
- as for documents i know btc-e doesn't ask for any, i also use bittrex and they never asked me for documents but i think for very large volumes they ask for it. and they are both legit places and never hold bitcoin hostage
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3. Yes. Mix through altcoins is a third way, which I had not organize and describe here yet. (I am engaged in this now). This way has some advantages (my thoughts about them I will write later) and a some minuses. One of them is that this way is, in fact, too complicated and you need to press "a lot of buttons."
In your case, you must register monero purse. Load btc to exchanger. Exchange btc to monero and then move them back into Bitcoin. As for the fees, they are quite acceptable. I looked through the shapeshift
Instant Rate 1 BTC = 96.4909903 XMR
Instant Rate 1 XMR = 0.01020749 BTC
Miner Fee: 0.02 XMR
That is for 1 btc the output we get: 0.9849. So the commission will be 1.5%. It`s acceptable, isn`t it? However, the extremely small size of the market spoils everything.
In your case, you must register monero purse. Load btc to exchanger. Exchange btc to monero and then move them back into Bitcoin. As for the fees, they are quite acceptable. I looked through the shapeshift
Instant Rate 1 BTC = 96.4909903 XMR
Instant Rate 1 XMR = 0.01020749 BTC
Miner Fee: 0.02 XMR
That is for 1 btc the output we get: 0.9849. So the commission will be 1.5%. It`s acceptable, isn`t it? However, the extremely small size of the market spoils everything.
not just any altcoin i said Monero because it has anonymity. any other altcoin for example LTC is going to be same as bitcoin.
the advantage is that you don't use a third party and can be sure there is no one to keep logs. but this is generally like the last step and the most fool proof method for some advanced mixing stuff and only suitable for those who want some extra advanced way and accept the complications that come with it.
although prices are pretty volatile right now but here are the calculations:
bittrex shapeshift.io
Exchange: 1 BTC = 97.7 96.75
Miners fee: 0.1 XMR 0.02