The startup time on today's systems is measurable in milliseconds. It's not necessarily true that a statically loaded program will load faster -- especially as processors become faster at much faster rate than disk transfer time.
Not necessarily, no. But usually.
A prime example -- perl. If you already have perl running in memory, the main perl lib is already in memory, so loading time of that 16KB segment and dynamically linking goes much faster than statically reloading 1.5MB of static code. Even a 100MB/s disk will take 15ms to read that static code. The dynamic linking of things already in memory could easily take <1ms.... Even if the libraries aren't in active memory, if they are frequently used, there is often a large disk cache on linux systems, so the file is likely already in memory... again, moving around in memory is something more on the order of microseconds than milliseconds...
No. If you have a process of the static binary already running, it will not be loaded again from disk but the same physical memory will simply be mapped to a new virtual address space for the new process. That's the time to set up a few MMU tables and you're ready. If a dynamic binary is already running, the new copy is unlikely to hit the disk for loading anything either but the linking still has to be done. Certainly much faster than waiting for the disk but still more work than for the static version. It could potentially be faster if the program shares large parts with other programs that are already running but itself hasn't been run before.