Code P0010, check engine light on?

This has nothing to do with the starter repair unless they damaged the intake oil control valve. I would clear the code with the scanner if it comes back then you will need to see if the valve has failed. I have attached the circuit here for you to see.
https://mitsubishitechinfo.com/data/GS41/2009/13/HTML/M113158140006500USA.htm

Hi

Wow, quick replies! Before I cleared the code, I checked and there were two more! P0442, C0700. I cleared it, turned off the car and started. A few minutes later, I got a P0004 and P0010. They did have to disconnect the battery in addition to the intake manifold. The only other thing they mentioned is that the air intact duct has a split in it that they "patched" since it can only be ordered through manufacturer. They said the split could cause engine to have erratic engine lurching (from excess air) - didn't have this issue, but maybe split wasn't big enough. Other than all the codes, the car runs pretty smoothly. I'll do more checks after your thoughts on the additional codes.
It's a small shop I go to for years, can't imagine them causing problems and not mentioning it. I don't think they like working on the Outlander though, maybe limited knowledge? They didn't have the computer necessarily to diagnose/fix when my ABS needed to be changed. I brought it to a dealership, they said ABS was bad, but it would cost a lot, I forgot, so I was able to buy a used one, replaced it myself and a friend that had a much superior OBD machine was somehow able to clear the ABS code. So that's the shop story.

Thanks for the diagram, JACOBANDNICKOLAS. I was trying to figure out if this was bird's eye view or looking at the engine (I deal best with color pics, hehehe). I removed he cover and just did some checking to see if *anything* is loose. Well, it was odd and it caught my eye. It was a hose clamp. Wedged vertically! Is this the one for the hose they said is cracked? The temporarily sealed it, but didn't put back the clamp. Could that cause the issues? Consequently, I just realized my pic matched your diagram, so at least I'll now have a better idea where the intake engine control valve is. I'll check next time I'm able (somebody else drives this SUV).

Hi, no problem. I'm just glad you're willing to help. I didn't put it back - it's too cold outside and I'm wanting them to do the work (I paid for it) and hope they'll be more vigilant (hopefully) in making sure everything else is good. Otherwise, it'd be what I did that could be causing the problem. Hope I won't get charged (you never know), in addition to dropping it off again and not being able to use the SUV. I'll keep you posted.
Makes me wonder how it would have ended all the way to the left side. Even if was placed on top of something and then it fell, I would likely put it on the right side of the engine bay. Unless the mechanic is left-handed.

Finally got the clamp back in, and was told they didn't see any other issue. Oil was low (driver did see a quick low oil pressure once), which caused gurgling(?) Causing the oil control valve error. I assumed they filled it back up which I guess I should check myself, since the p0004 and p0010 codes are back. One common fix is oil change, which it's due soon. It's too cold outside. I will try to check further connection. Weird about low oil is that it didn't look like there was any leak on the driveway. I don't necessarily smell burning oil or see blue exhaust smoke.

I have to sad I'm happy, sad and frustrated about all these. Happy because it's finally done. Sad because I have to stop going to this mom-and-pop shop. I considered writing a review online, but that can do a lot of damage. I will write them a letter instead detailing the events. Frustrated cause I tried to give them the business, and even after getting codes, doing my research since I didn't want it to be another cliche, then pointing out the clamp that was not put back, and mentioning that luckily nobody got hurt, after finally getting an oil change (and that they cleared the codes), after all those different days of not being able to use the SUV. There were still codes!
I'm not good with parts names and locations, but point me to a real pic (drawing is hard to interpret sometimes, especially if already zoned in to an area without another drawing of the big picture for reference), and give instructions, I can get it done. Anyway, I just figured I needed to address the Oil Control Valve part. But guess what? I saw the unclamped air intake hose. Still unclamp (I simply trusted that they put it back cause you know, it was a couple minutes job, but that I was hoping they check more regarding the errors)! I was appalled and livid. I also found the other end had a crack, and after a 2 minute search, found and ordered the part that they said was hard to find. I temporarily patched the crack with electrical tape, like they did, put a clamp and cleared the codes!
Seemed to work ok (never really had obvious operational problem other than codes), then codes came back! I went and figured I need to check the Oil Control Valve. But guess what? I saw the CPS sensor wires. Not even connected! There were no words. I put it back how it seemed to go logically and cleared the codes. Guess what? No more codes!
I also got the new intake hose and while replacing it, noticed a few hoses not pushed back all the way or not even clamped back. Those hoses are in enough to not cause issues, but come on, the bare metal is an obvious tell about its previous position.

I guess it's counted a day for each and every time I went there.
If something really bad happened, I hope the judge won't accept that the defendant was having a bad day.
Thanks for all your help. It's websites like this that helps people have like a second opinion.