(ii) 'He/she' and 'his/her'. When writing, that's the one I usually opt for, but I understand that some people dislike the clumsiness of it. When speaking in a situation in which I want to be very careful, I often use 'he or she' and 'his or her', but it feels a bit long-winded and maybe sounds over-fussy.
(iii) Using 'they' and 'their' as singular. I'm not keen, but I think this is probably the future. I notice that someone earlier on the thread wanted this. Probably there are now lots of people to whom this always sounds natural and right. Fair enough, but I just ask them to recognise that there are people who feel it's wrong or are confused by it. My mother couldn't accept that usage. It didn't annoy her. It was simply obvious to her that it was wrong. We could dismiss her response, since she was old (if she were still alive she would be 86 now), but only a couple of weeks ago I was with three colleagues, all aged over 40, but under 55, who were confused by a short piece of writing that used the singular 'they' and 'their'.