: 1, does Carrera 3647 have any marking between besides serial
: number?
It's a bit early to have the model reference as well, so if there is only the serial that's fine.

: 2, what type of crown it should be on this Carrera? Signed or non
: signed?
Could be either at this point. For a mainstream Carrera it's more likely to be signed, especially if Carrera 12 it seems, for a Dato 45 it would be unsigned. For a 3647 it's a bit pot luck.

: 3, how big is the original crown? In mm? ( the one on the watch
: seems in really bad shape)
6.4mm diameter and it should be relatively thin. If you look at the OTD gallery index page for the 3647, the first S index photo has the correct crown, but the N's is incorrect - it's much too thick.

: 4, how hard to get another lock ring with 1/5 marking...
Used to be hard, but a bunch have been on eBay lately.

: Still don't know how to post pic on here. :(
You need a "direct" image link from a photo host such as Imageshack or PhotoBucket. Paste that link here, highlight the whole text and click the button that looks like a painting. That tells the forum it's an image. Use preview not post to make sure it's showing correctly before committing the post.