1st time builder questions

You may want to check out Fursuit.org FAQ. It's a good starting place and has links to a load of other resources.

As for your questions, I'll try my best, but I'm sure there are others that could help you out more.

1) You would need to airbrush, paint or use markers to create such an effect, especially if you are looking for a smooth, continous effect.

2) I'm not to sure on this one. I've seen where people have used "weed wacker" line, fiber optic cable (bare) and even stiff fishing line.

3) This really depends on how you want the tail to look. Any of these method could be used, but your choice will depend heavily on how you want the tail to move.
a) You can create a foam core using stiffer foam such as that used in pipe wrap foam (which is something I've used. The foam can be cut and taped in such a way to give it the shape that you would like. This will provide a tail that is light weigtht and fairly durable, plus it will have some wag. [Can have lots of curve and has some wag]
b) Another method is to use a length of chain or heavy rope and wrap pieces of soft foam around it. This sort of tail will droop, but will also move quite a bit when shaken. I've also used this method (using a length of chain) and it works fairly well, but it really won't hold a particular shape (other than straight down). [Doesn't really have any curve, but will move around quite a bit]
c) A third method is to simply stuff the tail with filling (poly-fill or similar). This relies on the fur fabric of the tail to give it shape. It could provide a little more bounce, but probably wouldn't keep a upward curve very well. [Really this method will work somewhere between the first two option, depending on how you sow the tail]

4) There is a fur suppliers list here. You may be able to find something local to you. I've used both CR's Crafts and Denver Fabrics to purchase fur fabric. Many other supplies can be purchased at a local craft store (that may even cary a nice selection of fur fabrics) or Wal-Mart.

Again, I recommend checking out Fursuit.org as a good starting place and working your way from there.