Hey,
Welcome to the forums!
The way you're talking about these things is very definitional. There's nothing wrong with that, but I wanted to check that you're understanding what's going on here:
Crossing over:
You create new combinations of alleles on the one chromosome. This is super super useful e.g. if you have a "good" and "bad" allele next to each other you can separate them.
Random segregation:
Equally likely to get each version of the gene (I.e no allele favourtism). Again, this is super important so the offspring have a mix of traits.
Independent assortment:
Both a & b are talking about the same thing. The chromosomes line up on the equator independent 50/50 chance for each one what side they're on. This means when they get separated, they're independently sorted into gametes.
where this rule originally came from: getting allele A for gene 1 doesn't influence the likelihood of getting allele B for gene 2 (this applies as long as they are on different chromosomes). Otherwise, there would be relatively few chromosome combinations the offspring would be likely to inherit.
^ don't use these as formal definitions but I hope this helps your understanding