Flight instructor reported near miss with another aircraft and a helicopter while on approach.

Narrative

As a CFII I was acting as Safety Pilot for my student on an instrument training flight. The student was under the hood. After completing a practice approach at ZZZ I contacted Potomac Approach and asked for VFR flight following to conduct a practice ILS 23 approach at FDK. We were given a squawk code; were radar identified; were told to proceed to NUMBE intersection; were cleared for the approach and told to remain VFR. I noticed another aircraft on ADSB (but did not see them visually) approximately 500 feet above and assumed at first that they were VFR traffic conducting maneuvers since that is a well known practice area. However; as we intercepted the localizer and turned inbound; I noticed on ADSB that the aircraft above also appeared to be turning inbound (Aircraft X is a high wing; therefore it was not possible to see them above us). No traffic alerts were given by Potomac Approach. Instead; they handed us over to the FDK Tower. I contacted the Tower and told them our position on the ILS approach. The Tower Controller sounded confused and asked 'is this a practice approach?'. I answered affirmative and informed him that we had just been handed off by Potomac. He again sounded confused and asked 'you were talking to them?' I answered affirmative. He then said something to the effect of 'OK; I have another aircraft approaching from that direction- Aircraft Y. Report a 5 mile final'. At this point we were on about a 6 mile final which I reported. I then heard Aircraft Y report a 5 mile final just as it flew over us on final at about 50 feet. The controller then sounded really confused and said something like 'are both of you co-located?' I reported Aircraft Y in sight ahead and above and asked the controller if we should continue. He answered in the affirmative. However; I noticed Aircraft Y was now slowing down and we were catching up. I told the student to go missed just as the controller also told us to go around at the same time. The student began to execute the published missed approach which includes a climbing left turn. I informed the Tower that we were going around to the left in order to avoid Aircraft Y. He then informed us that there was a helicopter maneuvering just east of the Tower. I then took over the controls from the student and told the Tower that I would remain inside the Tower. I then saw the helicopter to my left about 50 - 100 feet away and below. I maneuvered between the helicopter and Aircraft Y and departed the area to the east. It seems there was a clear lack of communication between Potomac and the Tower as the controller seemed unaware that we had been cleared for the approach. The Tower Controller also seemed to lack situational awareness as he was not aware of our position with respect to Aircraft Y. I don't believe that Aircraft Y ever saw us when they overflew us on final since they are a low-wing aircraft. The Tower Controller also did not alert us of the helicopter to the left of the runway until after calling us to go around. He should have given us a right turn instruction for the go-around. In hindsight I should also have inquired to Potomac as to the status of the aircraft above which I saw on ADSB as soon as I saw it turn inbound; but I was distracted by the handoff to the Tower.