Can the phone fall off if accidentally pushed, does it have some sort of grip?

No grip, the phone has to be in the middle, and it is not easy to tip over.

Does this charger fold down flat for easy transportation in a bag, etc.?

its shape is fixed, it doesn't fall down.

doesn't come with charging block, is it supposed to come with the wireless charger?

no, it doesn't include an adapter.

I bought this a couple of months ago, it did charge my IPhone X but it will quit working and I have to unplug it and plug it back in to get it to work.

not sure it is normal, mine have the same problem.

the first time when I connected for the charge, this would not charge more than 40%..tried on different iPhone 8,iPhone x result remains same, is this defective?

fast charge my iPhone X

tip over easily?

no, it is stable

Does it work with S6? My S6 phone continually would reboot, hang, frewz up, etc. All problems stopped when I stopped using this charger

I have a s6 also, and it works fine with this charger, haven't met such problem.

Did not allow calls to go in/out while charging with iPhone X

I can send message with my phone charging

I just bought the charger and it doesn't charge my phone at all, any suggestion?

Is your phone compatible with wireless charging?

Will it work with samsung adaptive fast charger plug that came with the note 5?

Yes and it works no issues.