Issue:
Home built in 1972 and we still have original electrical panel. There are spots for 20 circuits, and currently we have 11 - 20 filled with a combination of single and double circuit breakers. Odd circuits on the left, even on the right. We have come to discover that multiple circuits can impact the same item. For example:
Circuit 15 controls a GFI outlet for a sump pump only.
Circuit 19L controls the clothes washer and dryer.
Circuit 19R controls a number of outlets in the kitchen.
Circuit 20L controls a number of outlets in the foyer, outside and upstairs.
Circuit 20R controls the garbage disposal only.

But when I flip off circuit 16, it actually turns off all of the items listed above, but just all of the items listed above, nothing else. Those other circuits don't "trip", but the items turn off.

Even worse, circuit 11 controls ALL of the items listed above (items on circuit 15, 19L, 19R, 20L, 20R) plus every light in our office, all outlets in our family room, kitchen overhead lights, gas stove and a few other outlets. In other words, when I flip circuit 11 all of what I described goes off. How can those items be controlled by multiple circuits?

When the clothes washing machine (19L) is pulsating, lights throughout the house on circuit 11 pulsate with it, even though 19L is a dedicated circuit to the clothes washer.

Somehow all of these things seem to be cross-connected.
What is going on?

Sounds like you have a split buss panel.
Show us a picture of this panel .
Circuits are usually label odd numbers on the left, even numbers on the right.
When you say circuit 20L and 20R are you reading the numbers on the panel
or are you just counting down the spaces?