Codes P0339 and P0300?

The most common cause I've seen for a P0339 (crankshaft sensor circuit code) was that someone put an aftermarket crank position sensor in, and it bent the connector pin sockets open just enough they don't make a tight connection. The next most common was that the sensor had corrosion under it that was enough to push it away from the reluctor wheel and that caused a drop out because of a weak signal. Both are very common. A bad lifter won't cause this code, but it can cause the P0300 if it's due to the typical hemi cam follower problem. That issue would cause the chirp you are hearing as well. The TC and transmission issue could be related as well.
For the sensor I tend to remove the bolt, pull the sensor out carefully so it doesn't break off in the block. Then use a rag to clean the bore, then I use a dauber with some silicone grease on it to block the sensor bore and then scrub the area around the bore with a wire brush and scraper to remove and corrosion. Then a bit of silicone grease around the sensor and reinstall it.

Check the sensor and clear the codes and see what comes back. I suspect the chirp is related, however we try to keep answers about different problems as individual items.