Incorrect. faizi is correct. If you use a FA disconnector with a three position safety the hammer will follow the bolt. You must either mod the safety, the disconnector or both. This is not an issue with a standard semi disconnector like the OP is using but some may simply buy a complete FA trigger group.
Sure... only if you're using an Auto disconnect. Simply, the vast majority of disconnects on the market are semi. I should have qualified my previous statement.