Firstly, many congratulations on winning the competition!! Well done!!
Referring to you post there seem to be a number of issues to deal with - firstly having a passport?? Secondly you need to obtain your "European Health Insurance Card" which will cover you for general medical care in EU Countries (including Austria) - information and how to apply can be found here
https://www.ehic.org.uk/Internet/home.do. You do not need to be approved for this, but just complete a form and a couple of weeks later your card will arrive.
Secondly to get travel insurance and using the links from this site is as good a starting point as any - they do seem to offer good cover/value for money. Only the insurance company will be able to tell you the level of cover and cost, depending on your health issues. The important bit is to remember to have included not only treatment there, but far more importantly that your insurance will cover YOUR transport home in case of illness/accident etc.
If you need to tell anybody about your health is mainly down to you, however you do need to check with the airline about what they might need to know about any health concerns/health issues you are currently being treated for and/or any medication you are carrying with you, e.g. insulin etc. You might need a letter from your GP to get through airport security a little easier - make sure you have the original but also several copies, as back up!
As for the hotel, all depends on what type of board you are on - but this hotel is (if I remember rightly) specialist in diabetic diets? So of course they need to know your preferences for food etc to be able to cater for your needs, especially if you are taking any other meals than breakfast.
I am sure others, will add their comments, but I think the above will get you started on the "paper" trail for your trip!
Hope you have a great time!!
Best
Alice