I'll answer your questions, based on the sequence...
1) If you get enlisted into NDU, you will do your BMT directly at
Sembawang Camp instead of Tekong
2) Remember, it's not only physically fitness that play the part...
Divers also have to be mentally fit as well... regarding posting
out, that depends, it'll be based on your aptitute and manpower
requirements of SAF, it maybe other Naval vocations, Rifleman
etc...
3) Divers are considered to be one of the toughest in the SAF...
What do you think?? Hell week alone is enough to kill... 
4) Yes, you'll book out during weekends like others unless you're
subjected to confinements or duties
5) Not necessary, there's chances of posting out after BMT and
thus, you've no chance to embark on the diving course... of course,
you may also make it to diving course but can also OOC due to
injuries etc...