I just installed the following:
-GTX3576r, clutch, flywheel, cmc
-Manifold, and exhaust system
-Intercooler, pipes, intake
-Pump, injectors
-I'm building my tranny by jacks soon

My question is do I have to build my engine?,
(if i have to, I'm going with Pistons and rods,and cams nothing more),
if i do have to build my motor, I'm thinking about cosworth everything (pistons, rods, cams), what do you think?

My only fear is that my car will be like my friend's, it takes a long time to start, and it doesn't run as expected, and i was shooting for a 10 sec evo.

To make the full potential of that turbo the short answer is yes. Everyone is going to ask your power goals are. If you keep the torque below 375-380 then dont build it. If you want to bump the torque up then build it. The 35r is going to be laggy anyway so I say build it and make the most out of the turbo!

I want cosworth cams, rods and pistons, nothing more, what do u think of the choice

Cosworth is a GREAT company, look at all the motors they build.

Personally, I am going to go with MAP heavy-duty rods, Wiseco HD pistons and GSC S2 cams when I do my build. Sticking with the non-sleeved 2.0 and going to be running either an EF3 on E85 or the precision 5858.

With that turbo I would do a stroker kit so you can spool that thing up quick!

Build it. Why half *** on such a perfect car brotha!

Do you think that my choice is good

No. There are better alternatives. You're going in a fun direction, but be sure to educate yourself along the way. There are very few questions you can ask that haven't already been answered. Start searching and reading.

Yes you will need to build the motor to reach the power levels you want for 10 sec timeslips. Your car wont have trouble starting if its tuned properly, but that will depend on the fuel choice. E85 will take a big fuel system and although that turbo is capable of making good power a larger turbo would have been a better choice do to the weight of the evo x.

Those choices of motor components are great.