Hi and Welcome to Lexus Owners Club Australia
In regards to the mats... make sure they have the clip holder on them and clip them in. They are renounded for causing sticky accelrator pedal as the pedal gets trapped under the mat... got caught myself once! not nice
Try ebay the the wheel cap
The ringing.. are you sure its not the belt? or it could be air con unit seizing up as it may have had little use. get it checked out by an air con specialist.. should not cost anything for someone to listen to it for you.