The top control arm bushings are likely candidates.
what model is ur integra? it could be a integra ls tranny or u have a integra gsr that comes with a gsr tranny
could not be getting spark our gas our timing belt no good
could it be the thermostat or the fan itself?
it could be the main assembly relay under the drivers kickpanel
check the fuel lines.. fuel relay, fuses, and if all else fails the pump.
problem could be the rear strut
no spark our timing belt snap our jumped timing
if its squeaking it could be to do with the suspension joints or the the suspension bushes, you will hear this mostly when accelerating, braking or going round corners. if its squealing all the time it could be your cam belt or the brake pad squealers, they squeal when they are too worn out and need replacing.
I tihnk it could be a head gasket but that's just me. The hed gasket's are placed uders they heads.
You could have a balljoint that is going bad or possibly a strut mount too.
Any B series engine will drop right in and Hasport makes a lot of mounts so you could probably drop an H22 or a K20 in.
When was the last time you had the suspension lubed? Did someone swap in some urethane bushings? They tend to squeak .