Check the belt going to the rear housing. Make sure it's on and tight. Make sure the fluid level is full on the rear differential. Don't try to put it in gear on its side. It has fluid drive setup on the later models. That's why you can slowly at speed or punch it nice and smoothly. Look at your owner's manual or if you don't have it give me the model and I can see if I can find it online.
First do a compression test. If the compression is good pull the codes and find the cylinder that is missing and switch plugs and erase the code and see if the mis changed cylinders then if that doesn't work try switching the coil and erase the code if that doesn't fix it then it needs a injector.
First thing rice does nothing except get stuck in the charging port. Never charge it. You need to immediately disconnect the battery and take the board out and dry it and clean any corrosion preferably in a sonic cleaner and hope it works. Once it's wet it can have hidden corrosion that can cause the phone to stop working at anytime. Or it may never have a problem.
You have either a stuck oil ring or damaged piston. You have oil getting into the combustion chamber. You are going to have to pull the heads off of the mower. It has something wrong internally. There is another possibility. Is the oil over filled?
Have you checked the see if the alternator is charging. If you put in a new battery and it runs for a few days and the same thing happens again it sounds like the alternator is not charging. You should learn to find out what is wrong before you just start throwing parts at it. You could probably had it repaired for less money if you had taken it to a shop and had them do it or had them at least find out what is wrong with it before they spent at least a couple hundred dollars.
What engine is it? Check the fuel pressure and make sure it at the correct pressure. How many miles on the truck? The timing chain could have jumped. Check and make sure you are getting spark. I need to know what engine and mileage if I am able to give you more advice.
You can disconnect the battery from the phone and it won't hurt it. Just don't disconnect the screen until the battery is disconnected. Changing the screen will not get rid of the apple logo. It's in a boot loop. It most likely has a problem from water damage. The problem is once they are wet they have problems for the rest of there lives IF you can get them working again. Most repair shops won't even work on them except to retrieve data when they are water damaged. If you want to try to fix it you need to pull the board out and remove the covers and see how bad it's corroded. Save the covers for the chips in case you can get it working. Once it gets wet it starts corroding and it does it faster if it has power connected to it. Did you try to charge it after? The first thing you should have done is open the phone and disconnect the battery and pull the board out and remove the covers on the motherboard and dry it off with a heat gun or hair dryer. Then clean any corrosion with a qtip and alcohol. See how...