Bicycle Austin forum

I'm a new cyclist and am besides becoming fit, am learning to deal w/ traffic.
I've started commuting from 2244 & Cuernavaca to downtown and typically I leave early around 5:30am.

How do you handle the the intersection of 360 and Bee Caves where the bikelane ends.
Do you leave the bike lane to move into the road behind the other cars?  Or do you ride to the end of the bikelane and merge/share the road as you cross 360?  (If for some reason I leave late, I'll typically go down to Westbank drive to Pinnacle etc to rollingwood.)

Coming back from work, I've tried a couple different routes.  I've gone down redriver/san jacinto to Town Lake trail; I've gone to 6th street to Town Lake.  What's the thoughts on riding down Guadalupe or Congress to go to Barton Creek(zilker park) to Stratford.

Finally, what's the appropriate way to handle intersections like 2244 & Cuernavaca.  The Bike Lane ends and is replaced w/ right-turnonly car lane.  I want to continue past the intersection though.  When the light is red, should I stop at the end of the bike lane.  Should I take the entire Right-turn only lane?  Or should I ride over but to the right of the lane so other cars can try to turn right and trust them not to get too close?

I'd really appreciate any help and guidance.