Are human chromosomes connected or separate molecules?
Each chromosome is a pair of distinct, separate DNA molecules.  A chromosome of an eukaryotic cell nucleus is a (long) helix of two linear molecules and so has two ends, which are called telomeres.  DNA naturally forms a double helix with its complementary DNA molecule, and the double helix can further curl in what are called supercoils.

In humans, the chromosomes occur in 23 pairs (totaling 46). Except for the sex chromosome pair, each member of the pair is identical in appearance in a karyotype (picture) and each such pair has a number assigned from 1 to 22; the numbering generally follows the size of the chromosome, with chromosome 1 being the longest.  In mammals, the sex chromosomes in a male are quite different in size and are labelled X and Y; a female has two identical X chromosomes.