Your eye needs to be centred exactly in the middle of the viewfinder eyepiece, otherwise you might well get some apparent shift.

Yes, but bearing in mind the downside of some shots with ultra wide lenses. There is a place for everything, but I rarely use polarisers. It all depends on your photographic style.

Yes, that does imply that you are using quite a wide lens. In 35mm terms I wouldn't use a polariser on a lens wider than 28mm, so in digital terms that is approx 18-19mm or so.

Just a word of caution about using polarisers with ultra-wide lenses. You will find there can be large variations in the depth of blue in a sky, for example, because the degree of polarisation varies depending on the angle with the sun. With an ultra-wide (even a 24mm equivalent such as the wide end of the 16-45mm) this effect can be quite odd and it does little to enhance the photograph.

I find that the ultra-wide angle tends to darken the sky anyway, partly because of natural vignetting in the lens designs and partly because of the oblique angle of the light.

Just because we're amateurs doesn't mean that we can't have professional standards. Always strive for the best. I'm sure that a cheap polariser, like anything else, can only disappoint in the long run.

It needs to be thin to avoid vignetting, be a circular polariser to avoid confusing the AF system and be optically and mechanically sound.

I would go for the best you can afford, without breaking the bank. eBay could be a good place to save some money.

Probably the only useful filter on digital is the polariser as polarisation is one of the few effects that can't be achieved after the shot is taken.

On film I used to use polarisers, 81A for colour and the usual colours for monochrome, particularly orange and red. All these things can be done in Photoshop with the exception of the polariser.

As regards protection of the lens I don't bother. It can only reduce quality, albeit only very slightly, and I have never ever damaged a filter, never mind a lens. There will be a first time, no doubt, but that's life. And that's what insurance is for.

It's not conclusive because, as you say yourself, it's not a very well controlled test. You need to use a tripod and ensure that the pictures taken are under identical conditions in every respect. That would also mean ensuring that the cameras are set up with similar parameters, nit one set on bright and one on standard, or whatever.

A detailed static subject under controlled lighting is best, and a flat subject too if you want to see if there is any fall off in performance towards the edge of the frame.

I've never experienced this problem with any lens, old or new. Are you sure that the coating has come away and that it's not just a discolouration of part of the front element?

This is one reason I shoot JPEGs. It eases the general sense of stress that I detect...

The simplest way to start is to at least use Adobe Gamma, which you will find under Control Panel on your PC.

It works quite well on a CRT, but I understand less well on flat screens.