Native-speakers generally use 'high' to talk about mountains. 'Tall' to speak about people. But 'tall' also to speak about trees, and some buildings (especially if they are high and thin). We would ask "How tall is the Eiffel Tower?" rather than 'how high'. Summary: For mountains, usually 'high'. For other objects, sometimes 'high', sometimes 'tall'. For people, always 'tall'.

'Higher' is probably more correct, but in everyday speech taller is absolutely fine - doesn't sound weird at all.

no you should use high it'd be mt.everst is higher than mt.fuji tall for persons

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“ Tall “ is only for persons not for mountains or things,,so you should choose “ Higher “ to compare these two mountains! Mt. Everest is higher than Mt. Fuji