Where can I find toyota carburetor for an AE82?

The best place to obtain parts for a vehicle that is young is the dealer, especially if reliability is paramount. That doesn't mean dealer parts are better than others but that is often the case. The best reason for opting for the more expensive dealer parts is the warranty, which is usually better than offered from the aftermarket.

The aftermarket is a source of replacement parts ideally suited to older vehicles and represents a considerable cash saving over dealer parts.
These are best sourced from a reputable local store.

There are parts finding a way onto the market that aren't fit for the intended purpose so it is important to be aware of this when sourcing parts on the internet - beware of really low prices.

Breaker yards are a good alternative source of parts. Some take a professional approach and offer a decent warranty on parts already removed and ready for collection or delivery. Others provide a field of dead cars and expect you to use your own skill and judgement to choose and remove the required part entirely at your own risk.

as the dealer said the sand will not degrade neither the reliability, nor its life duration

I take help from online websites that have this service like helping in repair some like reliable-store have instant help.. others are a bit slow which I don't prefer... rest is up to u.. U can also get free manuals

suggest that yo go to an accredited auto transmission shop and get a second opinion and quote the make a decision from there
there may be an after market part item ( toyota without the brand cost) that is used

CUANTOS CAMBIOS TIENE LA CAJA AUTOMATICA DEL
COROLLA AE82 1987 AUTOMATICO

head bolts for iron cast heads is 65. for aluminum heads, its between 45-50. 1.6 AE82 is iron cast.

I would double check the muffler side of the piston and make sure it is not scored up like this:
Remove the carburetor and make sure the intake side of the piston is not worn (missing more than 10% of the machining marks )like this:


If you do not see these failures and you have good spark the carburetor is the problem. see a local dealer like www.arcolawn.com for parts and support.

Goto this link http://www.scosche.com/ They sell wiring kits cheap.

under hood driver side

Im assuming its an 4AGE!?
http://www.ae92gts.com/ae92gts_valve_adj.html
And here one of my favorites...;)
http://www.billzilla.org/4agstock.htm