No need to turn it to position I, wait, then II. After the initial boiler fill the heating element is submerged so you can just turn it on to II. When a machine cools, the water in the boiler contracts lowering the level. When you turn it back on, the level probe calls for water to top off the boiler. That is what you are hearing. No water is being pumped into the grouphead.
Cleaning the screen. Yes, you will want to take it off now and then to clean it. It is held on by friction and the group gasket. Removing it every month or two will help keep it clean and keep the gasket from baking onto the grouphead. They can stick and require some destructive work to remove when they bake into the group for a few years.
There is a FAQ for the process and doing a forum search for "
e61 shower screen remove" will get you pages of information.
How to remove the dispersion screen and gasket of an E61?