You can join a series of lines into a polygon, and arcs into ellipses or circles. You may not join arcs and lines together since there is no one defined object that could represent such a group. To see if the endpoints overlap sufficiently to be joined into one object, select one of the objects, use "select adjoining" from the Edit menu, then select join from the Arrange menu. If you get one set of handles, you have succeeded.
Can I recreate an object once it has been unjoined (smashed)?
Yes. Select the object and select join. To make it easy to find the lines that make up this object, select one of the lines and select "select adjoining", then select join.