how long can this stay on for on new batterys?

If the question is: "How long will battery last"? A long time as I recall. Probably more than 6 months - seems the mouse may have needed to be replaced sooner but, it did not EAT batteries.

What is the max distance from the wireless keyboard & mouse to the computer?

I sit about six feet from my x-box and the keyboard works fine. I am not sure about the mouse though.

Questions & Answers: Rosewill Wireless Office Keyboard Mouse Combo

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Rosewill Wireless Office Keyboard Mouse Combo, Long Battery Life, Slim Sleek Ergonomic and Comfortable - RKM-1000

Wireless Convenience: Plug the wireless USB receiver into your desktop computer or laptop to start using both keyboard and mouse with a wireless range up to 32 feet
Long Standby Time: Maintain numerous months of keyboard and mouse battery life without needing to switch off each device; standby mode activates when idle, preserves battery, and allows you to resume working when ready quickly
Stylish Design: A modern, sleek and perfect duo for extensive productivity at home or the office; slim keyboard and clean mouse design maintains an uncluttered desk and workspace
Efficient Media Keys: Keyboard shortcut media keys save time by instantly opening favorite applications and web browsers at the push of a dedicated button
Ergonomic Mouse: Optical precision wireless mouse features smooth contours for a comfortable grip; overall symmetry for ambidextrous right and left-hand use

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