1) "by the fielders actions, the appeal can be made " is called a "live ball appeal" (any fielder).
2) "verbally appealing" is called a "dead ball appeal" so obviously the ball must be dead (no outfielders).
3) Yes, the runner is out for not tagging. Even if we could determine what the fielder knows or thinks, the physical touch causes the out.
4) The runner at home is also out. The umpire is only expected to be a mind reader when the rule specifically requires intent and that usually has to be accompanied by some physical indication.
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