For example, some leopards have a mutation which causes black fur. So Black fur and normal fur colour (orange-white) are both alternate forms of the same gene, right? So does that mean that mutations cause alleles?
That's correct. Alleles are alternate forms of a gene that occur at the same locus and arise by mutation.
Another example might be sickle cell anemia where a SNP (a single base change) is the cause of the disease.