LVM with SSD and SATA hard disks

LVM doesn't care what the underlying block devices are so you can mix any physical devices, or even software raid devices and it just works.

I don't see any points on doing so, you want a Volume Group that contains both SATA and SSD, that's possible.

Just create multiple PVs, with pvcreate /dev/partition_name

And create a volume group that use those PVs, with vgcreate

And do the partition of that VG.