If I were to replay an earlier mission in the campaign that rewarded me credits when it was initially completed, would it reward me credits again? This would be useful if I wanted to farm up all the upgrades available to me instead of being required to pick and choose between them.
You don't earn credits from repeating missions, but you can unlock achievements and earn research. Achievements unlock decals and avatars.
Currently I've finished all missions before going to Char and found that replaying some missions gives about 200k credits.
For instance, after replaying Breakout mission (I was out to get some unearned achievements) I've got credits when visited Research console.
He's talking about the credits you spend on upgrades. You earn them for completing missions and from completing certain bonus mission objectives. The exception is the Protoss missions, but those grant extra research to offset that.