I have asked this question here before myself. There are indeed specialist collectibles insurers out there who would be very happy to insure you, however when I made enquiries a couple of years ago of my own insurance company and explained what it was I was trying to insure, they really weren't concerned. This is because (for now at least; if prices keep going the way they are, this might change in the future) vintage Star Wars items do not meet their definition of 'valuables', which usually includes things like gold, silver, jewellery, fur coats, works of art, etc. As such therefore, even after explaining what I had in my collection and what it was worth, my insurers, Nationwide, said it was simply part of my household contents and didn't even require an itemised list. And when I switched insurers last year to Tesco Insurance, they said exactly the same.
Therefore, as long as the total sum you insure your contents for includes the value of your collection, you should be covered. Naturally I would strongly advise anyone wanting to make sure they're covered to contact their own insurance company to check, but unless Nationwide and Tesco are exceptional in this regard, you should hopefully be alright.
Regarding your other points, fortunately I have never had to make a claim on my contents insurance so I have no idea how either company mentioned above would act in the event of a theft, fire or other damage (you never find out how good any insurance company is until you have to make a claim, of course), however it seems prudent to maintain an accurate, up-to-date list of any items you own, together with good quality photos which clearly show their condition.
Hope that helps a bit!