In ST:TNG "Aquiel", Geordi reaches into the drawer in his quarters pulls out a phaser, and fires it at the organism. Aren't hand weapons on the Enterprise disabled? Are all officers allowed to have hand weapons loaded and armed in their quarters?
If you'll allow me to quote from the (considered fully canon) "Star Trek: The Next Generation: Technical Manual", the simplest answer is yes, you can operate a hand-phaser on board the ship, but you need to be a a command officer or a senior security officer in order to legally override the phaser controls which automatically set themselves to stun.
Downstream from the power cell are three interconnected control modules: the beam control assembly, safety interlock, and subspace transceiver assembly (STA). The beam control assembly includes tactile interface buttons for configuring the phaser beam width and intensity, and a firing trigger. The safety interlock is a code processor for safing the power functions of the phaser and for personalizing a phaser for limited personnel use. Key-press combinations of beam width and intensity controls are used to configure the phaser's safety condition. The STA is used as part of the safety system while aboard Starfleet vessels. It maintains contact between the phaser and the ship computers to assure that power levels are automatically restrained during shipboard firings, usually limited to heavy stun. Emergency override commands may be keyed in by the beam controls.
As to why Geordi has a phaser in his quarters isn't really explained. Other officers do occasionally demonstrate that they keep weapons lying around (Picard evidently has one in his ready room and both Worf and Tasha (albeit both were Security officers) evidently kept them in their bedrooms) but I'd guess that the out-of-universe reason was simply that having him go to a weapons-locker and come back was an unnecessary 30 seconds of filming.
You seem to be asking two questions here:
Are hand weapons on the Enterprise disabled?
The answer to that is a resounding 'no'. Think about the number of times phaser battles have occurred on the Enterprise throughout. One prominent example that comes to mind is when Worf uses the phaser to disable the Borg in The Best of Both Worlds Pt I and in Brothers when Worf and the security team are using phasers against Data (although there are force-fields in place there).
Are all officers allowed to have hand weapons loaded and armed in their quarters?
I haven't found anything on this on Memory Alpha, but from observation of the series, you don't normally see people walking around with phasers, unless they're security officers (not that they seem to help them most of the time anyway :P). Furthermore, most of the time on away teams in TOS, equipment like phasers would be provided upon departure. I seem to recall something like this occurring in TNG, but I can't say exactly where unfortunately. Picard in The Battle had a phaser on him when he destroyed the sphere and I seem to recall that he also had a phaser when he was in his quarters when he was paranoid about being revisited. Consequently, I would speculate (my apologies) that only senior officers and security personnel would be able to hold armed weapons with them in their quarters.