Internally my computer tells me the process takes about 5 seconds from the OS start to graphical environment but in reality there are several steps. For example this doesn't account for the period of time between hitting the power button and the OS itself starting to run, entering full disk encryption password, unlocking volume.
I would be surprised if a full restart actually took so short. Maybe not loading a menu or unlocking a volume is sufficient to explain the difference?
I will not start to count the seconds and fight which OS boots faster, but it is certainly much faster than it was in the nineties. Boot times are certainly one thing where modern computers have significantly improved. Everyone who compares an instant on 8-bit is oversimplifying things. Try booting to ie. GEOS on one of those.
This is not true. Are you still using a platter hard drive? (If an SSD, have you looked up benchmarks for it?)
My ~5 year old laptop used to cold boot Windows 7 in less than 10 seconds (once I'd disabled most autostarting programs, at least). It currently cold boots Ubuntu in ~5 or so; most of that time is spent displaying the UEFI and Grub splash screens. This is made possible _almost entirely_ by a Samsung Evo; I'm looking forward to getting an M.2 drive when I replace the computer.