Do you use it with LCD on all the time?

a) I think it has to do with setting on your dashcam. IIRC, gotta set to hotspot mode or something like that. Google for the answer.
b) Mine powers off too after I switch off my car ignition (similar to you unplugging the cable). To see if your battery is konked, start the camera without external power and see if it runs longer compared to the time it takes to shutdown when you remove the external power.

If you are the "got camera can already", then it better to buy the Power Edition since you are better off without a dashcam.
If you are the "will my dashcam help me?", I think it is better to go for First edition as the angle is wider and you will want to capture as much side way details as possible. Do take note that people have reported that the wider the angle, the less sharp it will be when viewing number plates.

Well, it's called a dashcam, isn't it? The battery imo is more to store the settings/configuration, and to allow it to save the last clip than to power the dashcam.

I would lower the angle a bit to record my bonnet instead of seeing so much sky. If you view your video, seeing too much sky makes the video a little distorted and cause giddiness. In addition, with such high angle, you might record very dark traffic videos if you are facing the sun in the evening time. You install the cam to record traffic, not UFOs, right?

You don't have to use all of it. In my case, I simply expose about 50% of the 3M tape which is enough to hold the camera and yet I believe allows it to be removed without any collateral damage. Just remember to black out the remaining unexposed 3M tape red portion using marker pen, so that it is not so obvious when you view it from outside the car.

Is it still recording? Iinm, yellow is charging indicator. Mine goes off once it's fully charged.

Yes, you are right, now I recall it.

1. it will delete old files (First in first out). I'd use a higher capacity card as too small a memory might cause frequent re-writing which may shorten the lifespan of the card - you don't want it to konk off when you need the recording most.
2. it works on WiFi to connect to the app on your smartphone. Do note that you need to switch on your phone "location" in order for it to connect.

I'm not sure how long the card can last. There are too many variables.

It's been said (read the posts in this thread) that switching off the WiFi will keep the cam slightly cooler. Heat is no good for lifespan of cam and the battery, and probably the uSD card too. You only need WiFi when you want to connect to your App on your phone.
I don't switch the WiFi off as I think most heat is generated by the recording.

How about playing the videos direct from sd card? Any issues?