How long does the battery last on the sensor?

Mine just needed to be charged after over 3 years and 3 months! I had forgotten that it was even chargeable it's been so long since I purchased it. I was surprised to see the charge port when I went to replace the batteries, so I checked when I installed it, August 2019. Works great!

Can I use regular batteries when rechargeable ones get bad? What size fit?

It uses a single 18650 rechargeable battery. Wires are soldered to battery and then plugs into circuit board. If you can solder, any 18650 can work as replacement. Battery is glued to circuit board, but with care can be removed.

Are the installation instructions available online?

Its actually quite simple. Put in the batteries, adjust the tone you want and the distance you want it to pick up on (we ended up taking it down and switching it higher after a week) with the two small switches inside the unit, screw on the back and swivel, pick a tree, screw it to the tree, walk by it 100 times to test it. (Make sure someone is in the house to let you know if it works from inside too), plug in the inside unit or put in batteries and voila! Its good to go.

can you program a time you want the sensors on or off?

Not that I know of - this is the simplest unit they have. However, you can determine the volume level of the base unit (the part that "alarms") or even turn the alarm sound completely off.