Using my own wood for smoking?
Ideally, wood for smoking needs to be chipped, probably using a wood chipper though you could do small batches by hand using a chisel or bandsaw.  Chips allows a greater surface area and gives a more consistent behaviour compared to large blocks of wood.

Whether you need to dry of not depends on several factors such as how old the wood is (I've never used apple or fig to smoke personally) and how much sap/sapwood it contains.  While I have not tried with green wood, I suspect it would just take longer to catch as the fire you put it on will dry it naturally.  Others on BBQ/smoking forums such as http://forum.bradleysmoker.com/index.php?topic=18832.0 say they have tried it and it works fine but obviously YMMV.

As for the bark - I would say for the smaller sticks where the bark is relatively thin then it's fine to leave on, but with larger branches I would remove it.  In some types of tree the bark contains more oil than the rest of the wood (e.g. Birch), meaning you will get a blacker, sootier type of smoke that is generally undesirable for smoking food.