The only really useful option is the present continuous in number 2. It is similar in meaning to 'I'm going to see him tomorrow', but suggests a more fixed arrangement. This is a very common way to talk about plans and arrangements for the future. You would only use number 1, the present simple, as part of a timetable. For example, you might say "OK, let's take a look at the schedule for Joe, the new trainee. I see him tomorrow, then he spends the following day with Mary in the marketing department, and then on Thursday ...'. This is a relatively unusual use of the present simple, and there is no need for you to try to use it - it would be just as natural to use the present continuous in this situation. As Rob has explained, number 3 is formal, rather old-fashioned, and rarely used in everyday speech.

Yes, you can. However the 3rd one is very formal and seems old. You would hear the 3rd one very rarely in modern speech.