How to remove engine from broken down 96 eclipse

you can line it up as good as you can with a dead blow hammer. make sure there is a small amount of oil on the inside of the balancer surface. then install the crank bolt and slowly zip it down with an impact wrench.

Yes by disconneting the map sensor will drop idle and make run rough, the problem is the idle air control valve or a vacuum leak, try to clean the throtlebody with an old tooth brush and some throtlebody spray cleaner if that doesnt help then try having the iac valve checked the iac valve (Idle air control valve ) if with the engine running listen for a hissing noise that will be a vacuum leak, these are the most common reasons for higher than normal idle. hope this is helpful.

Since you didn't specify if you had the turbo or non-turbo engine, i'll give you links to both.
2.0L non-turbo (420a) RS/GS
2.0L turbo (4g63) GST/GSX

Is there oil in the turbo?

before i start to explain how to replace this i cant stress this enough MAKE SURE THAT IS THE RIGHT COMPUTER FOR THAT ECLIPSE. the 95 non turbo eclipse has a different computer from the 96 to 99. and the gst and the gsx computers are different from eachother. the gst and the gsx computers are also different from the 95 and the 96-99 non turbo eclipses. when you get the computer i would bring your vin number to any local parts store or the dealer and they should know what to do with it. now that that is said. which computer do you need replaced. if your talking about the one inside the car it is located under the center console right behind the e-brake. removing that can be a challenge due to the several bolts that holds it on. you can use a phillips head screw driver but i wouldnt recommend it. i believe it is a 10mm socket that they will fix. after you get that off i would disconnect your battery. wait a few minutes than ground yourself out to the bracket holding the shift bar on(just grab ahold of it) after that is said and done there should be 4 bolts holding it on. (i believe 10mm cant remember) and a clip with several wires going to it. before installing. clean up the area around where the computer sat. remove any dirt or anything that may be there. check the clip that plugs into it for any damage, broken or burn wires, or if the plastic clip in itself is damaged. if not the dealer would be the only place to replace this at and i would strongly recommend a garage putting it in. if all is good installation is the opposite of removal. after you get everything together turn the car to the on possition with out starting the motor and let it sit for about 10 min. this will allow that computer to learn the way your car is set up. after that you should be able to start the motor with out a problem.
if you want the computer under the hood than its simple disconnect 1 or 2 clips and 3 to 4 bolts holding it on. inspect everything before installing the new computer along with cleaning up and dirt or rust in the area. and do the same process i explained about the other computer

oops sounds like you had the cam in the wrong place and bent a valve or two unless u mixed the cam caps and have them in the wrong spot that will bind the cam and lock it down by the way that is a dodge engine same as a neon

Hello, depending on which sender you have there will either be a spot towards the end that screws in to put a wrench on or if you have the round style I just use a pair of channel locks to remove it. I hope this helps.

If your planing on swaping the 2.0 non-turbo(420a) to the 2.0 turbo(4g63t) your problem will be that the motor and transmission are on opposite side of one another. My GST has the trans on the passenger side and the motor on the driver. The 420a is just the opposite. If your serious about it you should get the motor rebuilt with higher performance crank, pistons, rods, exc.  And they make turbo kits for the 420a.  But you'll need better fuel delivery and some mild tuning.

under hood, center, upper engine area, mounted on upper driver side of engine.

if you want to get rid of your MAF sensor, you will need to upgrade your engine management. there are a few piggy-back systems like MAP-ECU . you could also go with a stand-alone system like the AEM EMS