Maximum bomb load on any of the Spitfires was 1 500 lb bomb under the fuselage, and 1 250 lb bomb under each wing. However, I'm not sure if the Spitfire VIII was ever cleared for wing bombs. There's no technical reason why it couldn't have carried them, it's just a question of whether they did.
Did they actually have a 1,180 mi. range with full internal and external fuel load?
Depends on speed, but 1,180 miles was certainly doable. This is from an RAAF test of the Spitfire VIII:
The Spitfire VIII had 123 gallons internal, and could take a 90 gallon external tank.
And if it actually did carry more fuel than the other spits, why was it still lighter than the Mk.IX (fully loaded)?
In normal configuration (full internal fuel, ammunition, no external stores) the Spitfire VIII was heavier than the IX. However, later IXs had more internal fuel added, and the maximum takeoff weight was increased to compensate. The VIII had a slightly stronger airframe, and so could have safely carried more, but if there was no pressure to do so, it's unlikely they would have been cleared for a higher weight. Having said that, I have no idea what weight the VIII was cleared for. It's important to realise MTOW changed during the war for many aircraft, they usually increased as the war went on, and were reduced post war in the interests of safety.
I've read in
www.spitfireworld.com that the Mk. IX (at least late versions) had wing tanks AND a rear fuselage tank. If so, then why did all other sources say it only had 980 mi. of range?
Most sources quote a test they've seen, or an aircraft data card. The rear tanks were introduced late, and it's hard to find information on them.
Jeffery Quill tells in his autobiography of a flight he made in a Spitfire IX with rear fuselage tank and drop tank, from Salisbury Plain, up to the Firth of Forth and back. It was something over 1,200 miles, and he flew the whole thing at low level because of poor weather (range goes up at higher altitudes).
Your best bet for range is to look at the fuel, calculate consumption (and the Spitfire VIII figures above should be good for most Spitfire IXs as well) and work out the range from there. Don't forget to allow for warm up and takeoff, fuel used in climbing, combat allowance, reserves etc.
Conservative figures for a Spitfire:
Warm up and takeoff - 10 gallons
Climb to 20,000ft - 15 - 20 gallons
10 mins combat - 20 gallons