Any car can get abnormal mileage one way or another.
Short term exceptions high or low happen for everyone for any number of reasons... for short distances and time periods I've had as low as ~25 MPG ... and as high as ~250 MPG... the over all trend compared to alternatives I find tends to be more useful... the short distance and short term results are next to meaningless overall.
Extended term over larger distances and over longer time periods shows you more about the driving methods and proficiency of the person , and the over all abilities of the vehicle itself.
Because of what we know the potential of the I1 CVT has the potential for ... to get ~38 MPG, tell me a great deal about the low quality driving proficiency of the people who were driving it.
Being parked long term does not do permanent damage to the IMA battery , but it can lead to IMA error lights and reduced performance if the battery pack is not serviced.
I would recommend some healthy IMA exercise ... if it shows signs of issues ... you can look into the posts here at IC about doing the servicing yourself... or contact Ron at Hybrid-Battery-Repair.
As far as I know keyless entry is a standard feature that was included with All I1's STD or CVT.
Welcome and enjoy.