How to fix toilet

Even though you snaked the line near the toilet, it sounds like the line is still blocked or slow draining such that standing water sits in the line above the point of connection to the vent. Vent lines for toilets are often connected as shown:

Standing water above the reducing wye where the vent connects will cause water to be pulled from the toilet bowl as water flows down the line (such as when the other connected toilet is flushed). A flood when you flush both toilets indicates the sewer line is slow draining and cannot handle that much flow. Possibly the vent is plugged. More likely there is an obstruction such as tree roots infiltrating the line. If you have a septic system then it is time to pull the inspection lids, especially the one at the inlet. Check for obstructions such soap caked near the intake baffle.

If you have a plugged sewer vent or a plug in a line to the vent, then water can get sucked out of the trap in the toilet. I believe that this is the reason low water in the bowl occasionally occurs in plumbing that has no permanent fault.

I just poured a bucket of water into a properly operating toilet and the water drains down to a very low level in the toilet. So this is normal. The water supply system in the tank is supposed to continue a gentle flow into the bowl after the flush is finished to raise the level in the bowl to the height that the design of the toilet trap allows. In your malfunctioning toilet the water supply may not be directing the flow through the small flexible hose into the overflow tube. With the tank lid off compare a flush in the basement toilet to a flush in one of the properly operating toilets.