White smoke from exhaust, really rough idle, loss of power when accelerating, and smoke coming from passenger rear side of motor under hood. What could be the issue?

Sounds like water pump going bad.

sounds like you have a blown head gasket.

Sounds like a blown head gasket.

If you have excessive white smoke coming from the vehicles exhaust, it sounds like your headgasket is failing. Especially having a rough idle too. Check your coolant level, does your exhaust smoke smell sweet, like Antifreeze? If so, the gasket has blown. Hope this helps...

is there smoke coming out of the exhaust? if so what color? if it has white smoke is usually a blown head gasket. if it is a bluish gray it is oil. check your radiator when it is cool. if it appears to have oil in it it could be a blown head gasket. if you leave the radiator cap off start the motor, if you rev the engine and coolant shoots out of the radiator (compression from the cylinder forcing water out) it is a blown head gasket. this can cause the motor to run weak and idle rough and oil to disappear.
if you happen to have a compression gauge take out all of the spark plugs look at the spark plugs if they all look the same or is there ones that look black and sooty(running rich) or looks green(burning antifreeze/water) white Burning hot) http://www.dansmc.com/spark_plugs/spark_plugs_catalog.html
check the compression of each cylinder it is easier if you have an assistant for this. place the gauge over the spark plug hole crank the motor once or twice. the gauge should be around 120 psi (pounds per square inch). if all of the cylinders are under 120 psi more than likely you have worn or broken rings which will cause low compression causing it to run weak and consume oil.

it seems that the engine blew. the rings, rod bearings, main bearing etc. Sorry but it sounds like that. Especially the smoking at the exhaust. take it back to the one who sold it to you.If possible.

Check for antifreeze leak, make white smoke under hood, and check your antifreeze level

if its white smoke you have a blown head gasket.

sounds like you left something out. check to see if you plugged in all the sensors and plugs, then check for any vacuum lines that were not replaced or may have been broken

sounds like you may have had a head gasket failure, sorry for the bad news but white smoke from tail pipe = head gasket (big job)