Hi there Snowboy, welcome to the forum
I have a 2000 156, and the glovebox door is not a perfect fit on mine either. As long as it closes properly and doesn't catch I wouldn't worry about that. Also, I have found that the fan is very noisy (especially on the higher settings), so again I would say that shouldn't be too much of a problem.
Ah, Italian electrics
- this is something you will have to get used to. The headlights dim if I use the electric windows. The fan slows when I switch on the air-con. The dash dims if I so much as look at it. etc etc etc......
Not sure about the question with the alarm, but make sure that you get two keys. I don't think there is a master key on the '99 156 (there is a code instead, for the security system), but I'm sure someone here will correct me if I am wrong.
Most importantly, check the suspension and make sure it has a good history. The cambelt & tensioners should be changed every 36k/3yrs, so make sure this has been done if the mileage is at that stage (approx £400, as Wrinx said). If you are buying privately, make sure the owner has been keeping an eye on the oil. If they don't even know where the oil cap is, run away!!!
Good luck with your purchase, and don't forget to post some pics when you collect it