How to get to Tsukijishijo by 5am?

I am staying in Shinjuku area and would prefer to take the public transport to Tsujiki Market.

1. Does the oedo line operate before 5am?

2.Where can I get a train schedule of the subway lines?

3. What other alternatives are there?

Thanks!

1. Does the oedo line operate before 5am?

No.

Where can I get a train schedule of the subway lines?

Here you go:
http://www.jorudan.co.jp/english/norikae/

You can figure out the first connection of the day by selecting a very early time in the morning, e.g. 3am.

What other alternatives are there?

By JR, you can get to Shinbashi Station (Chuo Line and Keihin-Tohoku Line via Kanda Station) by 5am, from where it is a 15 minute walk to the market.

By taxi, I estimate it to cost around 2000 yen.

First train:
Shinjuku 5:02 -- 5:21 Tsukijishijo

Taxi ride from Shinjuku to the wholesale market will cost 3,500 yen with the night surcharge included.

http://tinyurl.com/42g7tv
S = Shinjuku
G = Tsukiji Wholesale Market