Do homologous chromosomes only pair during meiosis?

They pair so that they can exchange ge etic material so that at the end of the division, each sperm cell or ovum (which is the resultant of meiotic divisions, always) is different from the other three which ensures children are a mix of their parents genes (partly).

Mitosis, on the other hand, creates cells that are exactly the same as the parent. Why will they want to exchange genes? It'll ruin the process. So the answer is yes, they pair only in meiosis.

Homologous Chromosomes Pair Up During

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Yes they only pair in meiosis. Because your getting one chromosome from your dad and one chromosome from your mom. they are homologous because they have the same genes in the same place, however they may be coding for different allelles. For example, The gene for eye color is in the same locus as the gene for eye color in the other chromosome. However, one may code for blue eyes and the other may code for brown eyes, but still eye color!! They pair up so they can cross over and "exchange" genetic material in prophase of meoisis 1. The point of meiosis is to make four different haploid cells. In mitosis, the goal is to make exact copies!

Yes, during the process called synapsis. When they have paired up, the process of crossing over occurs where they change their genetic material. Crossing over results in new combinations of genetic material and is important source of genetic variation. This further creates gametes that have new combinations of genetic materials and enhances genetic variation among offsprings. You know right that meiosis occurs at gametes which are reproductive cells.