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Anytime you do any computer, sensor or major component replacement, you need to reset the system and drive the vehicle so it can relearn parameters and set all the monitors.
You need to drop your jag off at your favorite shop so technician can duplicate your complaint to be able to begin diagnostics. Sounds like your losing ignition or fuel pressure as things heat up.
Does it shift ok when the check engine light is off? Retrieve current codes and repost.
You must have a dual zone HVAC system in your vehicle, you need to have the blend door functions diagnosed and repaired.
Have you pulled the codes? If not, do that and repost please.
The check engine light blinking signifies a major failure, stop driving this vehicle until you get it properly diagnosed and repaired. A failing starter motor will not trip the check engine light nor will it make it flash.
Do you have any of the old sensors, have those tested to make sure they are defective. You should be looking for the cause of the problem and fix that. Have you checked the entire circuit? Check the connector at the sensor for loose or defective terminals. Do you get cam sensor codes? If so, what are they?
How many miles on your car? Has anybody checked the suspension and steering components, how about your drive axles?
The alternator checked good cold or hot? How many miles on this vehicle? The voltage regulator might be acting up.
With that age, mileage and water leaks your car is not worth spending much money on. I would just keep checking and adding oil as needed. Save your money so you can use it as a down payment on the vehicle I see in your future.