No, the number of chromosomes is actually barely related to complexity at all. For instance, humans have 46 chromosomes (2 sets of 23) whereas small deer have 6 chromosomes, and carp have over 100.

Though of course, a fish isn’t more complex than a human. Also a particularly striking example is the muntjac (a type of deer) where one species has 6 chromosomes and another one has 46 even though the animals are very closely related. And there’s a fern that has 1260 chromosomes. Some organisms have many copies of the same chromosome which also doesn’t increase complexity because it’s just the same information multiple times.

The underlying concept is that what is important is the information encoded in the DNA, not how much information there is or how it’s encoded. For instance, the number of chromosomes is based on how the organism happens to divide up its DNA. Whether the DNA is in 6, 46, or 1260 pieces, it doesn’t actually mean there’s more information. It just means the information is in many more pieces. A related note is that the size of the genome (the number of base pairs) doesn’t correlate with complexity either. This is because more information doesn’t mean more useful information. A lot of DNA doesn’t actually code for anything (as far as we know) so having more “junk DNA” doesn’t actually make an organism more complex. What’s really important is what the DNA encodes for and how the things it encodes for interact with each other. So complexity cannot be determined through the size of the genome or the number of chromosomes.

No. More complex organisms often have larger genomes, but there are some very complicated organisms with very small genomes and likewise some surprisingly simple organisms with very large genomes.

Some organisms with only 1 cell have lots more chromosomes than we do. Paramecium has about 50 pairs of chromosomes, and we have only 23 pairs!