Remote Support Software Resources

This tool must be connected to a good internet network otherwise it does not work properly, my question is how would that problem be solved if my internet is somewhat slow?

Is there a diagnostic tool software I can integrate like a process explorer or system explorer? Or is there an alternative to Techline that provides diagnostic tools and live chat and is reasonable?

I love using TeamViewer, but if for any reason, my computer shuts down (lost power, software updates, etc), I can't get use it. Could I relaunch Team Viewer automatically on set up? or turn my computer on remotely? or even if my computer falls asleep, I cannot user TeamViewer. Can i change a setting or something?