The closest thing you can do to seeing someone's activity on Ask is by following them. When you follow them, you can click on connections at the left hand side of your screen. After going to connections, you can see what questions they answered and which ones they asked.
If you follow a person on Ask, you can then click on "Connections" to see what Q's that person has answered recently. Also, you check out any questions they may have asked recently (on their profile page) by clicking on their pic. :)