The 2 options I think are worth toggling are the Volume controls (FXS I/O Gain) and the Audio option.
Both of these options are available under your vPanel > Features > Preferences.> Advanced.

I would recommend lowering the Volumke controls (both) to Very low or Low to suppress the echo's and feedback you're reporting. The majority of the phones we use today have built-in volume controls, use those instead to toggle the volume.

Echoing usually relates latency, seeing as this is the internet -- it will be sporadic. In this case I would try toggling between Audio Direct/Proxying through our servers if you continue to hear echoing on the previously selected Audio option - simply toggle this value.

If you're hearing beeps/tones, try toggling the DTMF mode option to InBand.
You may lose some compatibility dealing with other DTMF menus such as the automatted "touch key" systems you get when you call your utility providers, bank, ect. It's worth a shot though..