Is it safe to run and charge a deep cycle battery in an enclosed space like a bedroom?
Not "safe" without extra care. Death unlikely but likely possible if you "just do it".
Can be made "safe"
Discharge will not release 'fumes' in general use.
Risk from "gassing" (Gargoyle knows) can be kept small but not zero when charging with a panel of that relative size. ie 12v say & 30 Watt = 2.5A. 24V = 1.25 A. + say 3% and 1.5% ~ of bat 1 hour rate.
Small but non zero chance of Hydrogen and sulphuric acid fumes if battery not designed to vent unless 100% sealed with full recombination control. Ventilation would be an extremely good idea.
More if required ...
Long long long ago I charged a truck battery at a moderately high rate in a small closed room where I was sleeping :-). Took many weeks for my throat and nasal linings to "recover".
Data point: Just came across this [here](http://www.vonwentzel.net/Battery/00.Glossary/ ) while looking for something else:
Gassing: This is a very dangerous condition that can occur if batteries are charged too fast. One of the byproducts of Gassing are Oxygen and Hydrogen. As the battery heats up, the gassing rate increases as well and it becomes increasingly likely that the Hydrogen around it will explode.
The danger posed by high Hydrogen concentrations is one of the reasons that the American Boat and Yachting Council (ABYC) requires that batteries be installed in separate, well-ventilated areas." ... As the battery heats up, the gassing rate increases as well and it becomes increasingly likely that the Hydrogen around it will explode. The danger posed by high Hydrogen concentrations is one of the reasons that the American Boat and Yachting Council (ABYC) requires that batteries be installed in separate, well-ventilated areas." | From here | And ABYC site here
American boat and Yachting council website here
http://www.abycinc.org/
No open access data available on AYBC site - you have to be a member to read about how to be safe.
For what it's worth, cruising yachts have banks of batteries to provide electricity when the motor's not running while sailing or docked. They can be about as good an example of an enclosed space as you can get, there are ~30' boats that have tiny cabins where a bench may function as a booth when the dinner table is folded down and a bunk at night, and if you pull the cushions off the bench you find it's also the battery locker and you've been sleeping on top of the batteries.
Marine electrical systems are no doubt designed not to poison the occupants, but ventilation is not necessarily good on a boat (they limit the number of holes, for obvious reasons), so it is apparently possible to design these systems safely and there are people who live on cruising yachts for months or years. I don't have experience designing or working on these systems, but I think they might provide a good example to follow.
Re: Lead acid batteries in a confined space -- Any lead acid battery which includes flooded, gel and AGM batteries, will evolve H2 and O2 if overcharged too much. Sealed batteries use recombinant technology but are valve regulated, meaning that they will vent if the internal pressure exceeds the set pressure. Some batteries have captured vents that can be hooked up to a line to the outside and safely vented.