I bought a Top of the Line Fully Loaded EcoSport f...

I bought a Top of the Line Fully Loaded EcoSport from this dealer. Seemed Great other than NO CD Player available any more!!! BUT, soon the alarm started going off randomnly 2 to 5 times a day. I tried everything within my 73 years of serious auto knowledge (this is my 49th new car). I checked Google & Ford postings about this and could not find the problem; thus indicating that the dealer was going to have to get deep into it. I was first greeted by Service manager Jacquelynn Engles on how Ford does NOT have alarm systems any more & it is an aftermarket add-on sold by the Finance Dept. or installed by me so they are NOT responsible! I said that I bought this car from them just as it stands & the reply was that it must have been put on by someone else & the vehicle is an 'Unwind Sale' / Resale from someone else !!! I asked: "Then what is that lock button that beeps when I lock the car and that 'red noise cancel' (speaker) button on my Ford remote"? She said: "That's the Ford Arming System" !!! Arming what??? ...a Ford Alarm !!! I was told that this Fault has NEVER been seen before and there is NO information available on it BUT the Scan tool will show the event if it occured. Upon picking up the car 3 days later I was told that the Scan showed nothing and the 'Alarm' never went off when it was there. That day the 'Alarm' went off two more times AND 1 to 3 times every other day as I drive , park and lock the car! My car probably sat in the service lot unlocked (unarmed') that whole time and was NOT driven, locked & unlocked repeatedly! If the Scan Tool does not show the fault, then obviously it is not part of that Scan program. My employees & neighbours can testify to the problem.
Also, upon picking up my vehicles, I check Torque on all of the lug nuts after tire rotation. The Mag Locks were NOT torqued to spec. On a 4 lug vehicle that is 25% weak per wheel (and can be classed as 50% weak for that 1/2 wheel area (think about it)!

UPDATE:
Service Manager Joe Green responded many times to all the issues and solved them all...with a LOT of research & Discovery of new updated parts that addressed these seemingly strange issues. Random alarm and
flaky Remote Start was fixed -- the car DOES HAVE a Ford Alarm System; hopefully the Service Greeters were educated...always check the wheel nut torque yourself if you can!