1. Yes, it sounds like you are kerchunking the repeater.
2. Your ground plane is probably fine.
3. Your manual should tell you how to scan for tones. If it doesn't, use Google. AAMOF, Mr. Grinder above probably has a YouTube video on that.
4. Changing SQL isn't going to increase your range. If there is a constant problem on that channel, then yes, just skip it.
I would start by clearing all the tones, make sure the two HTs are seperated at least 100', and then see how they work.
Then work your way up from there one step at a time.
Edit:
Yes, he has a video on tone scanning. It is for the UV-5R but it might get you close.