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The P0420 is a catalityc converter failure code, P0440,441,446 are evap system codes, usually a loose or leaking gas cap, The P1135 is a malfunction of the air/fuel ratio sensor in the manifold near the firewall which is bank1 sensor1, the one in the front near the radiator is for bank2. Replacing the sensor usually takes care of this code. I'll be right back I'm going to check to see if there is any other information for the other codes.
Toyota has a technical service bulletin for the P0420 code, it involves replacing the ECM with an updated part but I would recommend replacing the A/F sensor first because it can affect cat converter performance, there is also a bulletin for the evap codes which call for the replacement of the canister closed valve(CCV) located on the air filter, I would recommend replacing the gas cap first and see if the codes come back, in case you need it the part number for the valve is-
The idle problem is usually related to a sticking idle air control valve, it's located on the throttle body, the throttle body should be removed and then the idle air control valve cleaned removing all carbon deposits from the moveable valve ond the housing, the throttle body should be cleaned at the same time,this also causes the hard starting condition you described.