Amp isn't needed but it will enhance the experience as the iPhone will meet the ohms rating these headphones have. The amp fiio e11 or e10 are both nice ones to look at.

First, no i don't think these need an amplifier. I have used these with my Samsung GS5, work and sound great.
The closest headphones that I compared to are Beats (don't like at all) , the upgraded Sennheisers, and the V-Modas. The V-Moda's are more expensive but have a higher bass response.

I believe so yes. In the least to hear anything worth while. I wouldn't recommend that dac/amp brand though. And if you're going to spend extra on an amp or dac, you might as well get the momentums which will work without any amp because of the low resistance, saving space in your pocket and wallet. You could still get a dac for any headphone if you're using an electronic music player with a subpar dac. However I think ipods have decent dacs, and my galaxy note 2 sounds just as great with my headphones as my expensive computer audio card. If you don't like the momentums the sennheisers 598 are much better choice on sound quality I've heard. You'd need an amp for those however as well.

I would say that you don't need an amplifier to use this with iPod unless you're an audiophile.

As for comparisons, check this article:
http://lifehacker.com/5800772/how-to-choose-the-perfect-pair-of-headphones

cnet.com is also a great place to research stuff like this.

A headphone amplifier is not needed but I would recommend using one for the HD558. I've played the headphones directly from an iPod and through a Schiit Asgard 2 amplifier (this is not a portable amp); the sound difference is drastically better via the amp. When I travel and not using an amp I will use a pair of V-MODA Crossfade M80's directly out of my iPod -- sounds fantastic. The M80's are a little bass heavy (at least compared to what my ears are accustomed to hearing, but still love the sound and like the relatively small form factor the M80's).

To answer the first part of your question ---- i don't think an amplifier is necessary to use these headphones with an ipod. I tried it with mine and it sounded good. Didn't have to turn the volume up any higher than i normally would (midway point). However, these headphones really came alive, as expected, when plugged into a stereo receiver with the included 1/4 inch adapter. But that's probably true with any set of headphones.

As far as what compares to it ----- i'm afraid i can't be of much help. For me, the Beats Pros sounded MUCH better. However, they clamp down on my head so tight that they are impossible to listen to for more than 30 minutes. And they cost $400, which is kind of ridiculous.

You will not need a headphone amplifier. You can plug these straight in to your iPod.
If you're a bass head, these are right for you. But if you don't like too much bass, I recommend you try out some Audio Technica ATH-M50s. There's not as much bass, but they sound pretty much the same (very good), but they are cheaper than the Sennheisers.

These are not Bluetooth headphones, so no. Sorry!

Sorry, the Sennheiser 558's are not Bluetooth capable. But a quick Google search will provide you with many brands and models that are. Good luck!

You could try using a headphone splitter and using a pair of headphones in one port and a soundbar in the other.... I'm not sure how that would sound, though.