I have a few comments based on all the other comments you've gotten. First, we absolutely need a better picture than this:
You don't need to be particularly flexible to get aero.
There are some basic things you can do that will *probably* reduce your drag, but you really need to test. You have a PM, so you can... It's also really good to get a cockpit that is easily adjustable. I'm not sure what you have, but if it's one of the aluminum PD T+ bars, then you are in good shape.
You appear to have long limbs, and if you don't have impingement issues, then don't worry about getting shorter cranks. At least not yet.
A saddle on the low side is better for aero drag.
Besides getting lower in the front, you can also reduce drag by getting narrower (shoulders). Extending the reach usually helps with this. Also, some people do very well bringing the hands up in front of their chin. Experiment.
Keep your head down as much as possible while still being aware of obstacles.
I'll 2nd what vjohn said about saddle position. It can influence a lot of things like weight distribution and muscle engagement. Triathletes tend to have a very forward saddle, but that puts a lot of weight on the arms and also makes it hard to utilize the glutes and hamstrings. Maybe that's better for running afterwards, though?
Since ideally you want your belly and back relaxed as much as possible, I don't believe "core strength" is important. But posture is. Try to minimize any unnecessary tension. Be aware of how the muscles engage during the pedal stroke, and practice relaxing everything but what's needed to make the pedals go around and hold your position.
Good luck! And have fun with it. Tweaking position can be a never ending process, but that's ok if you're enjoying the ride!