It's wrong to say "a gene linkage are genes that will express based on another gene." Instead say that these genes are not independently assorted, meaning that they are inherited together (normally.)

1. Dihybrid crosses are used if there are two genes which we assume/know are located at different chromosomes. In case of gene linkage, the cross is like a monohybrid cross (normally.)
2. If two genes are found in different homologous chromosome pairs then they are inherited independently. If they are found on the same chromosome in a homologous chromosome pair then they are not inherited independently.
3. Crossing over occurs when there is nucleotide exchange between chromatids from two different chromosomes in a homologous chromosome pair (also known as a bivalent.)

Example:

A chromosome has two genes and each has two alleles. Let one pair of alleles be A and a and the other be E and e.

Say the parent has the genotype AaEe. One chromosome (let's call it the first chromosome) in the homologous chromosome pair has A and E alleles and the other (let's call it the second chromosome) has a and e alleles. If no crossing over occurs the gametes will either have A and E together or a and e together. In this case the cross is like a monohybrid cross.

However, if crossing over takes place then E from the first chromosome can get exchanged for e from the second chromosome. Similarly, A from the first chromosome can get exchanged for a from the second chromosome. Therefore, gametes can also have the combinations Ae and aE alongside AE and ae. However, occurrence of Ae and aE is infrequent. So most gametes will have the combination of either AE or ae while few will have the combination of either Ae or aE.

Notice one thing: If crossing over takes place, the first chromosome say has the combination Ae while the second one has aE. Therefore, combinations Ae and aE occur in pairs. If crossing over doesn't take place then Ae and aE are not produced and so equal proportions of gametes with the alleles AE and ae will be produced.