Other than the straight vs Iambic key setting, I do not have any other suggestions. It might be RF feedback as that as gotten me in the past. I worked it out by using a dummy load vs an off center fed dipole. The dummy load did not have the delay issue.
On the not activating the transmitter, the only way that I know of is to install a switch (or separate fuse as I have) on the PA power supply line. That would allow for using the side tone to practice sending.