If a weapon is of the Slag element, does this make every bullet it fires of said element, or just the shots that proc the effect?
Judging from the damage-numbers colour, if a weapon is of the Slag element, this makes every bullet that it fires of said element. The same goes for the other elements, except for explosive, which always procs.
If I shoot a critter with the above weapon, and I shoot a burst of say 10 rounds, (ignore the mag size you see above) assuming round #4 procs the slag effect and is the only round to proc the effect, will the other rounds fired after round #4 do extra damage due to their not being slag, or will they count as alternate sources of slag despite not proc-ing the weapons effect?
If you shoot a critter with your illegitimate weapon, and you shoot a burst of say 10 rounds, (ignoring the mag size I see above) assuming round #4 procs the slag effect and is the only round to proc the effect, the other rounds fired after round #4 will not do extra damage due to their not being slag. I'm not sure what you mean by "count as alternate sources of slag".
Exception:
In Ultimate Vault Hunter Mode, [...] [s]lag on slag damage is also increased by 50%.
http://borderlands.wikia.com/wiki/Slag#Effectiveness
"By" is probably supposed to be "to", because 0% * 150% is still 0%.
TL:DR: If my slag weapon procs its slag effect, should I switch to another non-slag weapon or will my majority of non-proc-bullets be sufficient to make use of the slag.
If your slag weapon procs its slag effect, you should switch to another non-slag weapon. Your majority of non-proc-bullets will not be sufficient to make use of the slag.
Thanks to galacticninja for the extra information. ;)