As for the shaking problem (assuming it is running properly and everything is adjusted properly):
- it could be that when the engine was rebuilt, the rotating parts were somehow thrown way out of balance.
- maybe a weight was knocked off the flywhee.
- Maybe the front crank pulley has come apart - I've seen the outer pulley separate from the rubber isolator.
- The idle could be set too low (750 to 850 rpm with TE1 jumped to E1 is on the DLC1 engine room connector is normal)
- a valve could have been bent when the head was set on the block (or it stuck open when it fired up)- this will cause a lack compression and the motor to run on 3 cylinders (it happend to me the first time I rebuilt my 22re).
My guess is that it's the last one - do a compression test and find out if they all have 180 psi of compression or not.