Many questions

First, forget the presets.  They are there to demo  the capabilities of the HD500 and generally need a lot of work to make them work  for you .   You can get additional tones from Customtone (see the link at the the top of the page) or better still, learn how to build your own. If you are serious about understanding how to do this then there is some great information in the guide here, created by a community contributor - Meambobbo. It is heavyweight stuff but  there are test tones that you can use  as a demo  or for real --> http://line6.com/support/thread/71651 .  Between that and the Advanced manual (essential and  available for download from this site) you will be able to answer most of your questions.

The presence knob effects the very high  frequencies (above treble) and affects the 'brightness' of the amp model. This works well for some amps and sounds lousy on others.  More details on this in Meambobbo's guide.

The Master (in the amp settings) model's the behaviour of a master control on a real amp and does affect the tone as you describe.  The big knob on top just makes the pod louder or quieter without effecting the tone.  

On the amp:  people here use both real guitar amps and Full range Speakers quite successfuly.  It is generally easier to get a good tone from a real amp but when set up right the HD500 into a power amp can be very convincing.   The line 6 DT Series does what it says on the tin.  Personally, I use a Marshall JVM and it sounds great.  Other people use powered speakers such as a QSC K10 with great results. Yet others use a guitar power amp and that works for them. 

With stereo ... just be aware that it does not always work well on stage, where people will be standing around the room.  It is often better to concentrate on good mono tones.  Your call though and other people may differ.

It really depends on what you're planning on doing.  As TheWhites mentioned, if you're using a Variax and wanting to switch between electric and acoustic models, then you're better off going with the Full Range Flat Response (like a PA speaker) option.  The Line 6 L3t delivers a lot of versatility on that front.  When going with this option, you would run the full amp models in the HD500 because you'll be wanting the full amp, cabinet and mic modelling to deliver the final sound to go to the FOH.

If however, you're not using a Variax or only using the electric guitar tones and want to stick with a combo amp that could be used without the HD500 if you want to just grab an amp and go, then I would stongly recommend the DT50 (if serious gigging volume is needed) or the DT25.  What sets these amps apart is that they have been engineered specifically to deliver unmatched amp modelling realism.  The way they do this is by enabling you to have an analogue valve power amp section that can adapt itself to match the power amp design of the original amps of the modelled preamps.  When you use just the preamp model and select the right power amp configuration in the DT amplifier, it pretty much transforms the DT into the amp being modelled.  Not just the tone but the response and feel of the amp are very much like the originals. 

Some will argue that this can be done by feeding the preamp models into the effects return of any valve amplifier, but that's not really the case.  If you send a Vox AC30 preamp model into a push pull, class A/B power amp, you'll get crossover distortion characteristics that don't exist in a real Vox AC30 or if you put a Marshall JCM800 preamp model into a cathode biased (class A) power amp, you won't get that crossover characteristic from the power amp that is very much a part of the JCM800 tone. 

Which of these options do I prefer?  Both!!!  I use the Variax and switch between electric and acoustic, when I'm doing that, I play into powered PA speakers (like the l3t option).  When I'm only playing electric and want the mojo of some awesome amps, then the DT50 is magic.  I just love it when modelling the Vox AC30 or Fender Bassman, it's just like playing through the real thing.  If I want to just grab an amp and play without the HD500, then the DT50 with just the inbuilt amp modelling is a great "go to" amp.  I have a footswitch to select channel A or channel B, so it's plenty playable.  So, I can't say that one is better than the other because they aren't, they're just different and serve different purposes.

Anyway, there are quite a few things to take into consideration when making your decision.  All we can do is provide some pointers to help you on your way.

Cheers,

Crusty