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You suspect the loss of coolant is the petcock, but could be the issue discussed in the below thread. How are you measuring the temperature? Rough Idle When Cold/P0301 Code - coolant intrusion - TSB 22-2133 - Page 7 - 2.0L EcoBoost - Ford Edge Forum

I bought the below off eBay - it's not color but has everything I need. 2017 Ford Edge Electrical Wiring Diagrams Service Manual | eBay

If going with a different size battery its best to reset the BMS using Forscan, selecting the size and type battery.

I found this: Brake Pads R and I Front.pdf

Last time I considered that, the price was a bit of a shocker - where do you advise getting this?

No doubt that they're installed, but who knows how old they are? Please add it to your profile signature - https://www.fordedgeforum.com/settings/signature/

Do they show on the invoice? If they're on your invoice, check what kind of warranty they have. Please add it to your profile signature - https://www.fordedgeforum.com/settings/signature/

Unless asked, a tire fitment shop isn't going to install new sensors with new tires. The pro level tool that good tire shops have can also assess the sensors battery level. These sensors are very reliable, and when they go bad its usually the battery that's reached it end of life, which is around 5 to 10 years. Please add it to your profile signature - https://www.fordedgeforum.com/settings/signature/

What's the age of the sensors? No need to travel to a tire shop to do the Re-Learn procedure. $15 device is what I use. https://www.ebay.com/itm/363366733614 What is the Model and Year of your Edge? - please add it to your profile signature - https://www.fordedgeforum.com/settings/signature/

Its working for me, so suspect the issue is on your side.