Weird. The three errors are unrelated. The first one is related to the Extension Warehouse. There are at least a couple of threads on that topic already. Have a look at the forum. Having an outdated version of the Trimble Connect extension won’t make any difference to the operation of SketchUp.
The Fix Problems thing is related to problem geometry. That’s most likely due to the way you’re creating the model but if there’s nothing to fix now, then the geometry should be fine.
You could try disabling all of the extensions you have installed and see if that makes a difference with the drop down lock up issue.