So Conrad is 11 months now, and while I am amazed every day by his natural ability, he's really getting on my nerves with his constant whining and whimpering. Is this a common deal with this breed?

My guess is he wants to be with you and you have given in to his whining which has reinforced the behavior. You will need a good bit of patience and maybe some good ear plugs to break this habit.  I would start with the wanting in and out.  You need to control when he goes in and out.  Get him into a routine.  For instance, when you get up int he morning he goes out while you fix his breakfast.  After he eats he goes back out and stays.  He does not get to come in until he is quiet.   So if he starts whining you have to ignore it.  Only let him in if he is quiet.  Same for going out, he only gets out if he behaves.  When he wants out and starts whining, I would take him and put him in a sit and make him wait several seconds.  If he gets up, put him back in the sit.  Wait for him to be sitting and quiet, then tell him good dog and let him out.  Ignore the whining and do not respond in any way to it, not even to tell him to be quiet.  Negative reinforcement is still reinforcement.  I think if you trade the whining behavior for another behavior like sitting it will help, but are also going to have to ignore the whining behavior and it will eventually fade. 

Also, how much exercise does he get?  and how old is he?

Keep us posted on how it goes.  There are other things that we might be able to suggest too depending on progress.  Good luck!!

My GSP is 7 months.  She will definitely whine a bit here and there.  In most cases I find she is whining for a specific reason: in the car and needs to use the bathroom (long trips only), wants a drink of water, is overly tired, etc.

I second everyone elses opinion.  Don't reinforce the whining.  However, I do try to ignore her (no talking, or "it's ok...", etc.) while taking some indirect action to stop the behavior.  This may mean stopping the car to take her out...then right back in and on our way, getting fresh water, giving her some kennel time-out...I wait until she's quiet, if only for a second, and only then do I talk to her..."Gracie, let's get a drink, c'mon!"

I don't really mind the whining as long as it has some definite meaning and isn't excessive.  For the outside thing, I'd rather know she needs to be let out to "get busy" than having it occur on my floor.