heavy vibration of engine on idle

I would use brake parts cleaner on the metal components, and paint thinner on the plastic intake manifold. The throttle body cleaner would be OK on metal components that need a little lubrication, which is not the case with the pipes that you'll be cleaning.

This would be a great time for you to also replace the PCV valve as it is nicely exposed with the removal of the intake manifold.

 

The PCV (Positive Crankcase Ventilation) valve is used to ventilate the engine crankcase for emissions control reasons. It should be replaced when the odometer reaches 100K miles. The valve tends to get clogged over time as HC deposits form within.

The DTC P0441 probably was logged because the fuel tank has a hose which takes hydrocarbon vapors, passes them through the charcoal canister, and then leads to the intake manifold for combustion by the engine - and that hose is not properly connected to the manifold. So look for a loose or missing hose that connects to the intake manifold, near where the throttle body is mounted.

All gaskets that had been disturbed with removal of the EGR plumbing and the intake manifold should be replaced with new gaskets. You do not want any unmetered air entering the intake manifold, or exhaust system leaks.

 

The PCV should cost ~$6.
2010 Toyota Prius Parts - AutoNation Toyota Gulf Freeway Parts

I believe that there are several gaskets which seal the EGR hose connections?
2010 Toyota Prius Parts - AutoNation Toyota Gulf Freeway Parts

The intake manifold gasket should cost ~$16.
2010 Toyota Prius Parts - AutoNation Toyota Gulf Freeway Parts

 

This in particular looks bad. Where exactly is it?



Is it either at the intake manifold, or EGR valve, connecting to this pipe?



I assume so, but not sure exactly.

 

Are you thinking per Patrick, that it's air leak due to disturbed gasket? Pretty frustrating tho, if all interfaces clean and gaskets look fine.

What about mechanic's trick: spray WD40 at joints, and if engine speed varies it indicates it's being sucked in there.

 

Spray WD40 where there could be leak, at joints, gaskets. Engine rpm drops (or raises?), it's a sign the WD40 sucked in, there's an air leak there.

 

How would that method work on an engine with closed-loop control of engine speed?

 

I would advise using caution when spraying on hot surfaces, for example EGR plumbing. Potential fire hazard.

The assumption is that the leak is sufficiently large so that the engine ECU cannot manage the air/fuel ratio and the engine speed within desired parameters, hence a drivability issue is noticed. If the engine ECU was able to manage those parameters then the OP would not be concerned about a fuel economy problem.

In post #24 the OP reported a new DTC having to do with the fuel tank emissions control. This is highly indicative that the hose from the fuel tank to the intake manifold which carries HC vapor is either loose or damaged.

 

This photo shows one example of a gasket that should be replaced.
View attachment 81474

 

I'll abdicate, to folks here who actually know what they're talking about, lol.

 

The iridium spark plug change interval is at 120K miles. If this has not been done yet, do that now. You should not wait for a misfire DTC to be logged, to replace the spark plugs. You also should clean the throttle body interior and throttle plate, and the MAF sensor as suggested above.

The coolants should be replaced although failure to replace will not cause the particular problem you have noticed. The point of replacing the coolant is to prolong the life of the aluminum engine, inverter, and transaxle.