Noise & Vibration When in High Gear

Take it to a bike shop.

Very very difficult to tell without being able to look, see and feel...

However...Is the rear wheel properly centred in the dropouts?

Sounds a bit like very light disc brake rub. Put the bike on the floor, open up the qr, check the alignment of the wheel and retighten QR.

Also, the hub does sound as if it has a slight rumble which, as its a Boardman, is a common feature of the Formula hubs used in the OE wheels.

I'd concur with Dave's points - pics 1 and 3 look fine. 

Re: bullet 2 about chainline. It does look a bit as if the chain is leaving the sprocket at too much of an angle. It looks like it would be heading towards an inner (smaller) chainring - but you said that's it going from smallest sprocket to outer (largest) chainring...

If the chain is bobbing when you backpedal but not when you pedal forwards, it's possible that the rear derailleur is slightly misaligned. That's often more apparent when backpedalling. If it's only happening in the smallest sprocket it could be that the 'H' (high) limit/stop screw is a screwed in a fraction too far, or the gear cable is a little too tight (although that would probably affect shifting on other sprockets), or the derailleur/it's hanger may have gotten damaged/twisted.

I'm not sure it's any of those things though as they would tend to affect the chain at the back of the sprocket as much or more than at the front (as you look down on it). But your photo shows the opposite, which tends to suggest the problem is forward of the cassette, rather than below it. 

And none of the above really explains a droning sound or vibration through the pedals....

^ run not rub, haha that could be confusing!

the rubbing in picture 2 is inevitable because not all the sprockets can be lined up with the chainrings. It's nothing to worry about. The chain will rub smoothly when pedaling forwards as the rear mech guides it into position. When pedaling backwards, the chain will try to jump into the next sprocket because there chainline isn't perfect. I'd put some fresh lube on the chain and not worry about it. All my bikes make some noise in the workstand, and I'd be amazed if you could feel it over road vibrations when riding

That is an amazingly clean cassette and chain.   Lack of lube?

Wouldn't worry too much about the rubbing at the cassette if no noise when pedalling forward then.

Look for contact between the front mech cage and the chain. There should just be clearance in all gears, ideally, but you may have to use the trim function of the shifters to avoid it in some gears.

Also, some shimano chains can be put on the wrong way round which might perhaps cause this. See:

http://brimages.bikeboardmedia.netdna-cdn.com/wp-content/uploads/2012/11...

Further thought on 2: how many gears do you have in the cassette, and what chain are you using? (it will be written on the chain).

I wonder if you're using a chain that's too wide. Eg an 8 speed chain on 9/10/11 speed cassette.

On point 3, The different height teeth on the chain rings is fine. Look at the lowest ring here:

http://sheldonbrown.com/images/ramps-pins.jpg

This is one of the features (along with the pins and ramps labelled in the picture) that helps with shifting between gears.

On point 2, I am struggling to understand what you mean. It sounds very wrong. A picture would help. It doesn't sound quite like what you said, but if you're saying that the jockey wheel/pulley on the rear mech is in contact with the cassette through the chain in certain gears, then this is due to incorrect b-tension adjustment, and will cause additional noise. An excessive gap reduces shifting performance. This link will help you with this issue:

http://www.parktool.com/blog/repair-help/rear-derailleur-adjustment#arti...

Actually, the whole park tool website will be useful in getting your gears set up right.

On point 1, it is very hard to tell what you mean, but the shape of the teeth does vary, with differing bevels and recessed areas to improve shifting performance. This photo of a new cassette shows how the tooth shape varies from tooth to tooth:

http://www.hilarystone.com/images/sale%20images/cassettes/HG8-1.jpg

If your front mech is not quite adjusted right, it could be rubbing on the chain when in the largest and smallest gears in the cassette, sometimes it's hard to eliminate this completely which is why some shifters have a trim function. This would often cause rubbing a couple of time per crank revolution, as the pedal forces cause slight deflection of the cranks and chainrings.

edit: thanks for pictures. 1 and 3 look absolutely fine. 2 looks wrong to me, if there is actually rubbing, and could be a chainline issue.

It can be difficult to describe, let alone understand, these things in plain text so if you can't attach pics (or video) here perhaps try uploading them to a website you can share a URL to. But it sounds  a bit like something that needs a hand-on/in person examination.

On your third bullet point though - it sounds as if those are just teeth designed to help the chain move more easily from one ring to another, along with pins and ramps on the outer ring. But it should pretty obvious whether it's a design feature or wear/damage.