They only know that he was the one that supposedly made the order for the clones, but they don't really know because said person was supposed to be dead.

Following post contains material originally post on TFN. It has been modified to be an internal memorandum:
Repubic Senate
Memo
To: Darth Maul, Darth Tyranus
From: Darth Sidious
CC: Darth Plageous
Date: 3/2/0006
Re: Plan for Galactic Domination
As discussed in our meeting earlier this week. Here is my list/ plan.
1. Create clone army.
2. Find capable bounty hunter.
3. Get him to agree to be cloned.
4. We must be sure that all references to Kamino are deleted from every database in the known universe and especially CLONESRUS(TM).com
5. Make sure Dooku doesn't use his real name.
6. Be sure you don't pay with the "Emperor Palpatine" checking account
7. We must make sure Sypho Dias was dead.
8. We must make sure Dooku doesn't blab about the superior job he's done finding Jango Fett.
9. We must come up with 65 orders before "Kill all the Freekin JEDI"
10. We must make sure there was a reason for Jango to try and kill Amidala
11. We must make sure Jango takes the Job.
12. We must make sure Jango sub contracts a job he could easily do himself AND.....
13. We must make sure the subcontractor is a bumbler who will be caught by the Jedi so.....
14. We must make sure Jango can shoot the bumbler with(Not his wrist mounted blaster,or his shiny pistols) a poison dart from CLONESARMORUS(TM).com inscribed with just look us up in DEX.
15. We must make sure Jedi who gets dart knows who DEX is.(because Dooku did his job right)
16. We must make sure Dex still remembers Kamino (those Rishi maze days were a haze)
17. We must make sure Obi wan is smart enough to ask directions from a 5 year old Padawan.....
18. We must make sure that the jump to Kamino (which is NOT in the NAV 'Puter {traveling through hyperspace... you know the quote} doesn't kill the Jedi.
19. We must make sure Jango doesn't use the Kamino dart on the jedi when he shows up....
20. We must make sure his armor is plainly visible when Kenobi arrives.
21. We must make sure the Jedi informs the Jedi council that they've been blind sided by Sidous AGAIN.
22. We must make sure Jango is smart enough not to kill Kenobi on the landing platform. BUT....
23. We must make sure Jango is stupid enough to let himself be tracked to Geonosis, and....
24. We must make sure Jango is gullible enough to believe 1 missle is enough to kill a jedi and all his spare parts.
25. We must make sure Obi can pull that maneuver off without damaging his tramsmitter.
26. We must make sure that the Jedi Council knows that their Jedi has been captured, considering that..
27. The silly Padawan has gone off on some damn fool idealistic crusade to save his mother.
28. We must make sure the Jedi that shows up to pick up the initial order at will call has the convenient prepaid receipt (with the law firm of Palpatine, Sidous, Dooku, and Tyranus mysteriously blacked out.), so they can take possession of the source of their ultimate demise.



It looks much better in Word

I'd be willing to say that the Death star was started towards the (movie timeline) the end of AOTC or perhaps shortly after.
Then again how much time has past when we first see it at the end of ROTS?

Obi Wan isn't cold towards their deaths, they simply can't be helped, he doesn't oder clones to die, technically.. He doesn't order them to kill either.. Droids aren't alive.. Technically.. But anyway, the clones are there to fight (and die) for the freedoms of those who would rather not fight for their own freedom

In my post before, I meant to point out Grand Moff Tarkin was the overseer before Vader got his hands on it, Sidous's "Right hand man"