Did you manage to sort it out? No I'm using the standard charger provided but after charging it last night, the estimation of battery time in stamina mode has come down significantly. The estimation assumes stamina mode is not on but it is turned on in my notification bar. This time yesterday the estimate was at ~5 days.
Are you on a stock, as in not rooted?
The freezing happened to me when I was on stock, but since I rooted and running a custom ROM, I don't have this problem. I never had this problem when I was on stock either, only when I was on stock and used a magnetic charging cable. I think because I might have put the magnetic plug the wrong way around the first time (doesn't really fit though since the left and right plugs are different).
About the stamina mode, check your battery usage and see what is eating up all that battery.
If you're still on stock, maybe root and install custom ROM which might fix the issue.