TS wasn't a very fun game in skermish mode for reasons like this...good fun for the single player but everything else was annoying and slow. The original C&C, Red Alert, Red Alert 2, and everything since has been much more my style.
TS was actually very good online, better than RA in my opinion. It was still pretty fast paced (like the two games before it) but the sides and units were much better balanced.
Skirmishes are indeed faster and more fun in RA though. The TS AI is far more defensive than the RA one. I tend to play TS with the Eternity mod instead (one of the most crazy, WTF-inducing TCs I have seen for any game
You need the NOD CD in for the NOD missions and the GDI CD in for GDI missions. Its mostly because of all of the FMV they included.
There are several unused action videos on the CDs that are worth a look. You can use a fanmade program called XCC AV Player to look at them.
I wish they still had the action scenes in more recent C&C games. I used to love those. C&C and RA had a lot of them, TS had some but not as many, and RA2 and C&C3 basically had none.