Earlier quoted context omitted.
Only a little (as much as data will change during the backup). And default filesystems nowadays support resizing downwards so you can make space after initial partitioning.
You have to know in advance to not allocate 100% to root and home otherwise you are SOL when you want to make space later. If you're lucky you can disable swap and temporarily use its allocation to do it, providing that is large enough for the changes.
This is not the case, as like I said you can shrink either of those filesystems and its container and use the freed space for this.
(Also I think lvm doesn't need the volume blocks to be contiguous on the physical volume. So you might have N free space after volume a and M after volume b, and lvm would let you create a new N+M sized volume.)