Are the sectors in a cluster all next to each other?
Yes, a cluster is a group of contiguous sectors. The cluster size is the number of sectors per cluster, which is set when the filesystem is created (formatted) and cannot be changed after the fact without reformatting the filesystem with a different cluster size.
For example, an 8KB cluster size means each and every cluster on disk is 16 sectors long (assuming 512-byte sectors, which has been the industry standard for 30+ years now; very new drives use 4KB sectors, so an 8KB cluster size would be two 4K sectors long.)
Yes but clusters may not be