I'm trying to recreate the issues you are mentioning, and I think I may know what's wrong.
If I both have an object selected and I have the object in the smoothed display mode before selecting the insert edge loop tool, then after I select the insert edge loop tool it does not let me add any edge loops. If I toggle the smoothed display mode off, or even off and back on, then it fixes itself and lets me add edge loops normally.
If this is the issue you are having, you can either only add edge loops when the object is not in the high quality display mode, select the edge loop tool before selecting the object, or just toggle the quality display mode whenever the issue occurs (not something I would recommend since doing something similar on high-poly models often crashes Maya for me, but that may just be my computer).
As for not being able to click out of the tool, the insert edge loop tool acts like the translate or selection tool where they are always active until you change to another tool. You can't click out of them, so you would have to change to a different tool or just press Q to get back to the normal selection tool.
Sorry if I didn't explain this well or if these don't solve your issue, please let me know if so!