Nikon D40 with 300mm lens AND teleconverter (Nikkor AF-S Teleconverter TC-20E II)

I'm very close to purchasing a Nikon D40 - my first SLR. My interest
is birds and wildlife so a high zoom is essential.

My questions are:

1. Will a 300mm lens and a 1.7x teleconverter give me 510mm zoom?

2. What "optical zoom" number is this equiv. to? (I'm used to a
generous 15x on my Fuji bridge camera)

3. Will autofocus still work?

4. Would I be better off getting a super zoom lens in the first place
(though this option looks VERY expensive)?

Be gentle with me - I'm new to photography.

Many thanks

Greg
.