They are considered an anomaly in the game. Only ships with a Survey module are able to open/investigate them. Once we go gold modders can change this of course. Other options include adding warships in fleet to your survey ship.

As of Beta 5 (some) Anomalies will be guarded by Pirates and will kill off your ONE and ONLY survey ship if you do not do something, either not send him to the Anomalies or add warships with him in fleet. 

Okay.  Next question:  Are there any plans to make them stable (and therefore usable by other ships)? Or is that also something than has to (and can be) modified in?

Stable wormholes would be extremely valuable: both strategically; and (quite possibly) economically. 

Well, maybe not.  Initial survey ships now have attack/defense so you might survive.  Might not, as well.  But mine survived it's first battle at least.