I'll try & answer some of your questions, as best I can, so far as I know, others will have specific knowledge.
A David Jane article in Military Modelling Magazine (soo last century) said to add a 1.5mm disk behind the brake drum on either the front OR rear axles, not both. I can't remember which, but it is to make the track width of the wheels the same.
Would the ammo storage boxes have only lime coloured fronts and the back, bottom and sides black?
... Not sure what you mean, The Fixed storage bins bolted to the deck would be the camo colour as the body.
Extra Ammunition were in steel or wood transport boxes, typically SCC Brown.
If you mean interior primer, RAF Interior green was used in aircraft and early (Pre 1939) RAF contract vehicles?
Primer, if used by Bedford, would probably be Red-oxide.
... I'm 95% certain these vehicles were only used in the desert, & would have desert camo.
After they were not needed, they were converted back into 3-Ton General Service lorries, but kept the soft-top canvas with the dent in the roof, and were paint in European Theatre colours, Green & Micky-Mouse ears black camo.
What was the base colour under the lime colour?
...Don't know for certain. Bedford painted the chassis black at factory.
Did the differentials have a (half sides) white back?
... This was for convoy lights at night.
Only the rear differential was painted white, and was lit at night with a bulb. I'm not sure when they started doing this.
Was the AT gun more often carried at the bed or, more easily, hooked at the back?
... Guns were 'Porteed' (2pdr, 20mm Breda, 6pdr) for these reasons:
Speed, a towed gun was considerably slower in travel & couldn't keep up with lorries or armour.
Usually, only Infantry regiments were issued with towed guns.
Wear & Tear, as above, fast towing a gun risks damage.
Speed, a porteed gun could be brought into action, firing forward, or more often rear-ward, much more quickly.
Firing the gun on the truck, put the chassis under a great strain, so was done sparingly, & this was combo was replaced by the Deacon 6pdr.
The gun could be demounted for ambush or pre-prepared positions, but at 2,520 lb (1,140 kg), this was only done when needed.
It could be, and was towed, but the truck was also be used to maneuver the gun into position.
More info here: Portee
Was all personal gear also loaded on the truck?
... Think traveling circus, including everything a crew would need, and tea making kit!
A 6pdr crew was nominally 6, Gun Commander, Aimer, & loader, supernumeraries were ammo handlers, so lots of gear.