In my house its sounds like the sump pump kicks on and sucks the water out of the toilets lowering the level. It does this often, maybe once or twice a day. Does this sound familiar to anyone and is this harmful?

It is installed wrong, call the plumber.

I'm attempting to figure out the connection between a sump pump suction line and your drainage system. Are we talking about pump that drains water built up in the basement due to rain or groundwater intrusion,(sump pump) or are we talking about a gray water or sewerage pump that pumps the discharge from a basement bathroom up to a overhead sewer line? (Grinder pump and pit)? Talk to me, Tom

Tom, with the lower, shallower traps in the new toilets, they are easily pulled dry. A disposer or washing machine or dishwasher or sump pump causes the waste to move so much faster that it helps to pull the toilet dry. This is why those items are not legally able to be connected upstream of a fixture or within 10 feet downstream of a fixture.