IPhone – Does iPad mini 4 also feature the new and faster 2nd-Generation Touch ID sensor featured in the iPhone 6s

No,

iMessage and FaceTime are linked to your Apple ID so you will need to add your Apple ID to the device, not your phone number.

If you send a message from the iPad it will use the Apple ID, so someone can reply to your email address, if they send a message to your phone number it will only go to your phone.

Having just googled, I can't find a definitive answer to your question.

However, intuitively, I'd say that I can't see any way that, with a finger, you could select a point with accuracy anywhere close to 264 pixels per inch (see the Display section of the iPad technical specs).

And none of the Stylus reviews I've seen (such as this recent one from The Verge) suggest that any available styluses/stylii can reach a significantly greater accuracy than a finger - presumably because of the capacitive nature of the display: see e.g. this from Wikipedia

Capacitive touchscreens are more expensive to manufacture and offer a significantly lesser degree of accuracy than resistive touchscreens.