Is this manual flash okay for a begginer to photography, with a nikon d3000?

Http://www.amazon.com/Yongnuo-YN-560-Speedlight-Flash-Canon/dp/B004GZLFHM/

Also are grey market lens okay to use and what is the difference between a 300 mm telephoto lens and a 300mm telephoto zoom lens?

Maybe.

How willing are you to learn how to adjust the exposure with the flash manually each time you take a shot?

There's NOT a big difference between the cost of a gray market or full US Warranty camera.

Links:

Import (gray market)

http://www.bhphotovideo.com/...300mm.html

USA (full warranty)

http://www.bhphotovideo.com/...300mm.html

You will have do decide for yourself. If it NEVER has to be repaired, then maybe the savings is worth it to you, but as you look through the lenses for sale, you can see that sometimes there's NOT that big a difference between the two.

The difference between a Prime/Fixed focal length 300mm lens and a 300mm zoom lens is that the 300mm fixed is going to get you better quality photos because it's made for that exact distance. As for the 300mm zoom has an advantage because instead of carrying a range of lenses you have a zoom lens which covers various focal lengths. Prime lenses are usually cheaper too because they have less moving parts.