Yes, you can. You can also hook one up to a sulky and it will outpace a harness horse. This I have seen. But, I haven't personally experienced riding or driving one.
That's an interesting question. I have never seen an ostrich ridden or driven and have no idea where they would even do that. I know they hunt ostriches in Argentina.
I have only seen ostriches ridden on TV. I see how this is possible, but I think they are kind of wild. I would be afraid to be pecked. I don't think I would have the patience to train the ostrich even if I could get over my apprehension.