First of all, the info above about NECK SIZING only is accurate. Full length pushes back the shoulder and reworks the brass to excess. Headspace is almost irrelevant with a rimmed round, after the first firing in the same rifle, the case is fireformed to that chamber. 5 to 10 reloads at full power (174gr FMJ and 39gr 4895 for me) is typical. If you don't want to buy a .303 neck sizing die and you also reload .308 Win, try a .308Win die, that will, when adjusted, size only the neck of the .303. It will hold the projectiles a bit tight but thats OK.
Headspace- for the .303 case the rim thickness, min 0.058" Max 0.062"
For the bolt Min 0.064 Max 0.074" (British military dimensions). You can immediately see that a combination of Min/Max rim and bolt gives a headspace of 0.016"- a condition that the victorian engineers were very comfortable with. So should you worry ?. If it passes the 0.074" gauge (that is, it does NOT close on the 0.074" gauge) it is safe to fire. Just DON'T full length size the cases!!!.
The question about firing .308 bullets - most of these are boat tailed and don't work too good with a bore that may be 0.003 or more larger, stay with .311 bullets. The flat base upsets better. 123 gr 0.311 pulled bullets from the Russian 7.62 x 39mm shoot quite well at 100yds, just remember that bullet quality is what accuracy is all about and some of those pulls are not good quality - 6" groups with 7.62 x 39mm at 100 yds must be due to the bullet. As for cast bullets, first, the rifle must shoot OK, that is be properly set up and accurate anyway- most .303 are not properly set up. They need to have - tight bearing against the rear of the butt socket-firm contact all around the action- firm bearing of the recoil shoulders(the lugs that have the two pins for the trigger sear and the magazine release) against the corresponding part of the stock-absolutely NO TRACES OF COPPER in the bore if you fire cast bullets. The cast bullets need to be .313-better is .315" -LEE 180gr or Lyman 314299-gas checked and well lubricated and also lubed with LEE liquid Alox. Fired at a moderate velocity by say 19 gr 4198 or 18 gr 4227 or 24gr Varget. Most of my .303 respond well to that averaging 2" x 3" 10 shot groups at 100yds and my best is a 1912 SHtLE with a very pitted Australian Heavy barrel fitted in 1952 that does 1.5" x 1.5" 10 shot groups at 100yds. Incidently, it shoots like that after me spending over 1000 cast bullets through it to find out some of the items above, starting out with 6" groups at 100yds. I used the same 30 cases all the time and lost 2 from case shoulder splits.