I can take a stab at what I've learned so far, but technique is the most varied aspect of piano playing and hardly anyone agrees on it. Here's what I've gathered, addressing your points along with others:
1. Start with posture. The head, neck, and torso should be aligned (this does NOT mean straightening the natural curves of the spine) and, at the start, balanced over the "sit-bones" (sit on your hands, you'll feel them). The torso moves as a unit, we do not break the alignment though we may tilt left and right, forwards and backwards. This does not mean rigidity or tension, however.
2. Playing should be done first with the upper arms (in combination with the torso), then with the forearms, then the hands, and finally the fingers. What this means to say is that we often use the smallest parts of the mechanism (the fingers) to do things they shouldn't/can't do. For instance, fingers do not locate the keys, this is done by a combination of upper arm and forearm. Fingers do not shape chords, this is done by the stretch of the palm muscles. Fingers often don't even press the key down, the upper arm, forearm, and hand are all capable of doing so in various combinations. Fingers serve as an extension of these larger bones,
allowing them to do their work.
3. Any tension is always at impact. When you press the key, your muscles tense for an instant, and then relax. Once you have played the note, you can do nothing more than hold the dampers up, and the weight of your arm will be fine for this (or the pedal). Excess pressure into the keys is called "keybedding" and results in slow play and tension. So, to answer your question, your arms are not tensed throughout the playing, it is a tension at impact and then immediate relaxation. You must tense to play the keys, but you must not carry over this tension to the next key depression.
4. The combination of the forearm, hand, and fingers form a natural arch, simply by their structure (See Freeing the Caged Bird by Barbara Lister-Sink). If we maintain this arch while playing, it allows for maximum power to be transferred from the upper arm and torso to the keys. If we break this arch, we cut off the power from the larger bones of the mechanism.
5. Your wrist question. Position of the wrist has nothing to do with the keyboard. In fact, position of the wrist is a result of forearm flexion/extension and hand flexion/extension. When both are extended (to a certain point), one can draw a trace a straight line from the knuckles of the hand over the back of the hand and arm to the elbow. When both flex, an arch forms as the forearm rises and the hand dips. From what I have seen so far, there is no reason (and it could be harmful) for the wrist to dip below the alignment point during extension, but I have to verify this. Either way, extremes in wrist position are to be avoided, as they do cause tension.
6. Play with the fingertip or the back of the hand? I have no clue what you mean by back of the hand. You don't play with the fingertip, you play with the joint that connects the finger to the hand. This allows freer movement and faster play.
7. Round hand. Yes. This is in keeping with the natural arch statement before. You can either get the feel by holding a tangerine, as you say, or if you hold your hand as if you have a baby bird or a delicate flower in it, and then turn it over. Notice that while the fingers are curved, it is not extreme. The fingers may curve more or become flatter while playing, but there is always a slight arc and they never curve to the point of paralysis.
That is by no means complete, but I hope it helps.
Topic: The best/right way to play piano