When does cellular respiration occur? are there any situations where living cells are not respiring?

Cellular respiration occurs in the mitochondria, the double membrane organelle. It occurs when the cells need energy, storage molecules like glycogen are rapidly broken down from being a polysaccharide to its monomer units which undergo reactions once transported to the cells requiring energy and broken down to release its energy.

Yes, there is a situation where living cells are not respiring. For example in the microbial cell that lives in anaerobic environments in specific environments will use fermentation instead of respiration to produce ATP. The example of this is the yeast cells in beer mash.

Ithink the dna sequences may vary but the amino acid sequences are identical.