Apple

I have a few questions about my Apple TV 4k, which I’ve owned for the past 6 months now. I have paired it with a mid range 65 inch Sony Bravia (4k with HDR).

1. If I use HDMI 1, I get this warm tint (which I like) and makes it feel like HDR (I have the setting at 4k HDR 60). The interface feels very smooth, and there are no issues while viewing. However, when I turn on the TV using the Apple TV remote, one of the following will happen randomly- a. Only the Apple TV turns on while the Sony TV is still off b. Sony TV also turns on, but detects no signal from Apple TV, and takes me to the default screen. I have to manually change source to access Apple TV c. Both of them turn on and everything works fine

2. I tried using the E-ARC HDMI 3 (since I read about it being better for HDR and Dolby) for the Apple TV and faced 2 issues- a. The slightly warm tint went away, even after colour balancing and having the same settings b. I felt a slight lag in my input on the remote and actually seeing the thing move

Is there something I need to do to ensure the TV always turns on and goes to HDMI 1 (best case scenario)

OR

Is there some setting I need to check for E-ARC?