This is the case almost always, however, there are a few arguable exceptions such as Abomasnow, Ground/Rock mons, and Steel/Rock mons where the amount of weaknesses they gain are not worth the dual Stab and elevated movepool.
depends on a lot of factors. can the Pokemon utilize both its types effectively? BSTs in the right spot to make the Pokemon work good? wide move pool? wide move pool and BSTs good? the ability of the Pokemon?
It depends on what Dual Types. For example, I'd rather have Grass over Grass/Ice, because the latter has many more weaknesses. I'd also prefer pure Steel over Steel/Rock, as it doesn't have 4x weaknesses and a weakness to water.
On the plus side, some dual types are very beneficial, such as Water/Ground to Water, Water/Dragon to Dragon and Grass/Steel to Grass.
As for offense, it may or may not matter. Having a rarely-used offensive type as STAB wouldn't really make a difference in offense if it was added to a pokemon. On the other hand, something like Rock/Fighting can get very good coverage.
Offensively, a second STAB can never hurt but may never be used (for example, Dialga never bothers using its Steel STAB).
Defensively, you have to look at the type chart to figure out how much damage the Pokemon will take from each type. A good way to tell how defensive a type is is to take all of the multipliers for the different types and add them together. The lower the number is, the more defensive that type combination is. For example, a Fire type takes x1 damage from Normal, x.5 from Fire, and x2 from Water, so it would add up to 3.5 for these three types.
Now this isn't a perfect way to calculate how defensive the type is because types like Poison aren't used offensively often and Ghost attacks have a lower base power than Fire attacks. However, you can do more math to weight each type appropriately. In general, though, if the number is lower for the dual type Pokemon than the single type one, that secondary type has made it more defensive.
Generation 30: The first time you see this, copy it into your own signature (on any forum) and add one to the generation number. Social experiment.