Final answer:
The organism described is a type of yeast, which is a fungus, capable of living indefinitely in haploid or diploid states and used as a model organism to study cell processes. It can reproduce both sexually and asexually and has a short generation time.
Step-by-step explanation:
The organism described can live indefinitely in either a haploid or a diploid state, mutants are available for every gene in its exceptionally small genome, and it can study various cell processes, which points to it being a fungus, specifically a type of yeast. This is because yeast can reproduce both sexually and asexually, making it a versatile model organism for studying genetic processes. Yeasts have a short generation time, and their cell cycle is capable of alternating between mitosis and meiosis depending on environmental conditions, which is different from the much longer cell cycle of human cells.
Considering the details provided, the best description of this organism is option B: It is a fungus, since fungi can display a life cycle that alternates between haploid and diploid stages. This makes it an ideal model organism for the reasons stated above, rather than any of the other options listed in the question.