Although the 13A Plug can take 1, 2, 3, 5, 7, 10 and 13amp fuses only the 3 and 13 amp are normally used. So 0.75mm to 1mm cable should have 3 amp fuse and 1.25 and 1.5mm a 13 amp fuse. (0.5mm rated at 3 amp but min cable allowed is 0.75mm Table 52.3)
The manufacturers will know the right size to put in, so if it comes with 13Amp fuse in the plug that will be fine. I've never heard of a 15 Amp fuse for a uk plug - 13Amp is the biggest I've come across.
5) If the fuse does blow, then an electrician could have a look at the wiring and deem it capable of supporting 16amps (see (2) above) and replace your dedicate oven connection on the wall with its 13amp fuse with a new one with a 16amp fuse, and thats probably fine especially if it is a dedicated circuit from the switchboard. If the electrician looks at the wiring and decides its not capable of that then i guess you'd need to get a new cable run from your switch board to the oven which would mean digging up your walls etc so it might be easier to find the lower wattage oven.
Fuses are designed to break the electrical circuit when they are overloaded, so should there be a spike in current the fuse should blow rather than your equipment. If you use a 13amp fuse with a product designed for a 3amp fuse, it will work, but should it go mad and draw more current, the fuse won't stop it, and you WILL damage the item, and it poses a serious fire risk.