Can you have two planeswalkers out in play in magic?

Answer 1

Yes, you can have two planeswalkers in play, so long as they do not have the same name or type, otherwise they are subject to the Planeswalker Rule.

If you have two planeswalkers with the same name or type both of them most be discarded.

You can't have two Planeswalkers with the same 'type', meaning you can't have both Ajani Goldmane and Ajani Vengeant in play - while the two cards have different names, both are 'Planeswalker - Ajani', and would both be destroyed because of it.

Answer 2

Yes, just as long as you don't violate the Planeswalker Uniqueness rule. You cannot have two Planeswalkers of the same subtype on the field. So you can have Jace the Mind Sculptor and Gideon Jura out in play at the same time, that is fine. But you could not have Jace the Mind Sculptor and Jace Beleran out in play at the same time, both have the subtype of Jace, to show both are the same person. In the same way as the Legendary rule stops two of the same Legendary being in play at once, the Planewalker Uniqueness rule will send both Jaces to the graveyard.