Upgrade sub panel

Hello all, I'm new here and i came here for some help. I live in Queens, New York and im living in a two family house that was built in 1925. All wires in the house are BX/AC cable (no ground wires). All electrical boxes are metal. Half of the second floor is wired to the main 100 Amp, 2nd floor panel in the basement. The other half is wired to a 40amp sub panel located on the second floor. I would like to upgrade the 40amp sub panel to a 100amp sub panel. This way i can re-wire the whole 2nd floor to the sub panel and not make any home runs down to the basement. The wires feeding the sub panel are 8/3 stranded copper BX/AC (no ground). I know i will need to replace the feed from the main panel going to the sub panel. Some questions i have are,


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1) What size wire should i run?
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2) Do i need to run conduit from the basement to the sub panel because it is such a large wire?
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3) Do they have BX/AC cable with large wires that can be used?
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4) Currently there is NO ground anywhere in the sub panel. With the upgrade, do i need to run a ground even though everything in the sub is BX/AC no grounds?
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