1) Is it permissible to shake hands or hug with women who have reached advanced age?

2) Is it permissible to hug our Tayi ammi, Maami, Chachi?

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Ans1) Yes there is no harm shaking hand with elderly woman as long as intention is not for lust.
Ans2) Tayi Ammi, Mami, Chachi all they are non mahram so the rule is same as for other non mahram woman.