Jack pretty much covered everything. but here is a little more
What determines battery voltage at full charge? the type of battery and how its made also as an effect, ie even the acid water ratio, but sealed and unsealed batteries, type and amount of materials etc.
To find full charge when you get a new battery, fully charge it with a good 3-4 stage charger. The reason I always say that it must be charged by a 3 or 4 stage charger is this, convertor may charge the battery to 90 % if you leave it running for 4 weeks or so and do not use anything on board. So called automatic chargers may do very slightly better in less time. The only easy way to fully charge a battery (and rapidly) is to use 3 to 4 stage charger.
You mentioned flashlight batteries, if they are disposable they are intended for one time use and damaging the internals by over discharging is not important. If they are rechargeable taking them right down shortens their life dramatically ( but everyone does it so we dont notice how much longer they would last )
The DVD player, I have measured many many appliances, TV's that are plated at 55 w generally use less than 40w in normal use ( the plated rating is hard to achieve even if you switch volume colour and everything way up) so if you ever measure its consumption you will likely find it is less than 35w.
Lets say for example that the only item you ever run is 2 amps consumption and your battery is a 100 Ah battery. if the battery is fully charged, you could reasonably run the item for 25 Hours (25 hrs X 2 Amps = 50 Ah), so you are getting maximum use from the battery and the battery will remain in active and happy service for many many years.
If you were to charge via the vehicle alternator, you would be extremely lucky to get 70% of fully charged, therefore max "safe" useable power is 20 Ah ie you couls use the item for 10 Hrs Max. If this is the only charging that the battery ever gets, you would be lucky if the battery lasted 2 years even though you have not over discharged, the reason is sulphation, battery power is a chemical reaction as you use power the plates form a layer of lead sulphate, if the battery is fully recharged this lead sulphate turns back into sulphuric acid, if its not fully recharged then the lead sulphate eventually hardens and becomes charge resistant.
The above leads to 3 simple rules
1. Always use a good 3 or 4 stage charger.
2. do not over discharge the batteries.
3. Always fully recharge as soon as possible.
Apply the above rules and you will get much greater use from the battery between charges, much longer years of service from the battery before replacement, you will save the cost of the decent battery charger over and over.
There is a 4 th rule avoid "charging via an Alternator" this one is much harder to explain, but say you fully charge your battery by Shore power at home, if you drive to your destination with the battery connected to the alternator, the battery will be at 65 to 70% by the time you arrive.
There is a simple experiment that proves this, say you have 2 batteries one fully charged and one discharged to 50% connect them togethor in parrallel for a while and they will try to level out, when you come back say a day later the 50% will have gained charge and the 100% will have lost charge. Even if you add a trickle charger the 100% will still lose charge.
I did the following experiment and had the following results.
from fully charged at 12.93v (measured 12 hours after coming off the Sterling charger) connected bulb, it took 6 hours and 17 mins to reach 12.2v (ie flicking over backwards and forwards from 12.3v)
It was then fully recharged on the Sterling, allowed 13 hours to settle the voltage, reading was 12.94v flash 12.93v, the engine on the iveco was started, then I connected the battery using a good solid cable as before and drove this morning for 1 hour 14 mins, as soon as I got back it was connected to the same bulb (55w halogen) connected at 12 : 12 today, it started flashing between 12.3 and 12.2 at 5 : 37 PM today
Same battery, same full charge by Sterling, only difference 1 hour 14 mins of extra "charging" as knocked off 52 mins off usable power !!
Note Sterling is my good 4 stage charger.