/run contains all sorts of virtual stuff, it doesn't persist over a reboot,
I would advise against deleting anything in it as those files are used by programs running as whether user has the ID of 1000 (most likely you)
it contains things such as sockets and lock files so that programs can interact with each other
partitions are used for organizing, the downside is that more partitions make each one smaller
I end up running 1 btrfs partition sagred between all my installed Linux distros on one system
lvm is also awesome for resizing and moving partitions
my desktop right now has nvme0n1p1 as my efi partition and p2 as a lvm pv
inside that lvm I put everything else as it's very easy to resize and move them (I also have p2 encrypted with luks2)