1. Do all the River tiles need to be laid, or just those drawn until both the spring and the lake have bookended the river?
2. If the River tiles are played before the base game tiles, is the original start tile with the darkened underside placed into the draw bag with the rest, or does it have to be the first one laid after the river has been completed?
1. All River tiles are laid. The starting tile is the Spring. The Lake is kept to one side. Players then each place a River tile, extending the River. The River must not flow back on itself (no 180 degree turns (U-turns): see CAR for further explanation). When all River tiles have been laid, the Lake tile is placed (no followers can be deployed to the Lake tile at this stage of the game), finishing the River. Play now continues as normal with the base tiles, but see the answer to your second question, below.
2. According to the current CAR, "the original starting tile can either be mixed into the stack of river tiles, or placed as soon as the river has been completed, and is treated like a normal tile."
The current CAR can be downloaded from this thread:
http://www.carcassonnecentral.com/forum/index.php?topic=587.0