How can I determine where meiosis occurs in the life cycle of a plant?
All of these terms are just names for things that existed long before someone named them, and although you can figure out some of the ploidy from the diagram, you need to know the terms/definitions to complete it all.

Sporophytes are just the name for the diploid cells of a plant/algae that reproduces through a haploid life stage called a spore. You could consider the zygote almost like it is a "special sporophyte" from the perspective of ploidy: it's only special because it's the first cell assembled from two haploid cells. All of the other sporophytes are produced from mitosis from either another sporophyte or from the original zygote.

Being diploid is nice because you have two copies of every gene, which is more robust to mutations (while also maintaining genetic diversity for later generations), and, crucially, it lets one organism make a variety of haploid spawn for sexual reproduction.

Maybe you are wondering just about the terms haploid/diploid, and why "2N" vs "N"? The important thing is it isn't just the total number of chromosomes, it's the number of COPIES of each chromosome: with N you have just 1 of each, with 2N you have two of each. The important thing is that they are homologous, it doesn't matter if N is 1 or 2 or 40.