2. YES. For starters, if you have a UEFI install you MUST have an EFI partition. Opinion is divided on whether to have a separate /home partition (I have one) and there are valid reasons for having other partitions.
3. NO. If you really want to setup all your programs from scratch when moving from one major release to the next, that's up to you. It is one of the reasons I have a separate /home partition.
Your partition setup shows that you installed LM20 with the 'erase and install' option on a legacy boot drive. You have a useless EFI partition and mint has put the / partition in an extended partition.
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Unless you are saving to external media mounted in /media/you or to a NAS you don't have a choice, everything else is owned by root.I save absolutely everything in /home.