Aggressive Puppy?

Being tangled in the leash is probably frightening for him and he reacts by nipping.  Nothing you've said sounds like any sort of agression to me, and honestly, at this age its going to be VERY rare to find a truely agressive pup.  What it does sound like tho, is that HE has you trained and he is getting very spoiled.  not a good start.
 
Keep a leash on him at all times.  When he goes to get into something and won't respond to leave it (which is an invaluable command that you need to teach NOW) you have the safety of the leash to gently remove him from the situation and your hands are safe.  I'd be getting this boy on NILF...nothing in life is free....right away.  Want to go out?  Sit.  Want to be fed?  Sit and wait.  Want an ear scritch?  WORK FOR IT.  If you use the idog search and type in NILF you'll find all sorts of great guidelines.
 
You're a first time dog owner and you got a terrier?  you've got your work cut out for you.  Terriers TEND to be tenacious little dickens and they need to know that YOU are in charge not them.  And I don't mean by using aversives or being mean, but simply by being a benevolent leader.  NILF is a GREAT starting point.  But, get yourself to puppy classes ASAP, and then basic obedience and keep right on going to classes.  This is gonna teach YOU how to teach your dog.  Look for a trainer who does positive reinforcement....you don't want all the ancient traditional alpha roll, rub his nose in poop kind of stuff......you want POSITIVE REINFORCEMENT which basically is getting your dog to do what YOU want him to do cuz he wants to please you and not out of fear.  Anne is a trainer and hopefully she'll see this thread and give you some help.
 
If your siblings are under 10, don't let them be around the pup without your supervision.  Little humans are the most bitten simply because they ARE little humans and pups see them more as littermates than alpha.
 
I'll email Anne and if she's on today, she'll be along to help.

Is this an indication that he is going to be a very aggressive dog?

 
At this point, all this probably indicates is that you have a rather typical confident little dog with lots of attitude.  This is not normally a pup for the novice owner, but you can make him successful if you get started right away.  My advice would be to get him into a class with a positive trainer who has experience.  You can find trainers at [linkhttp://www.ccpdt.com]www.ccpdt.com[/link] or at [linkhttp://www.clickertraining.com]www.clickertraining.com[/link].  Ask about their experience with singleton pups, or pups that leave the litter too early, and with your breed.  Go to a class in advance and watch.  Classes that have puppy playtime beforehand are excellent.  Try to sign up asap - don't wait.  More pups die in shelters because of behavior than end up dead from diseases.  To keep him from chewing on his leash, you can spread some Vicks Vapo Rub on it (sprinkle a little Alum on, too, if necessary).  Do not tug with him at this point.  It's fine to get him an appropriate chew toy and substitute that for whatever he has in his mouth.  Do *not* pull things out of this pup's mouth, and do not leave him alone with young kids.  Instead, teach him to "trade" (look in the archives - I've given the method before).  This is a dog that will need consistent training, so that he knows the humans are in charge (nicely, of course).  If he gets nippy (most puppies get nippy, it doesn't mean he is going to be dangerous unless you let him "practice" it) just withdraw all attention and leave him alone, even if you have to put the bathroom door between you.  Encourage kids not to run or screech.  The quieter the household, the quieter the dog.  HTH

Thanks Anne.  It's always best to have a real pro weigh in!