Would using 185/65 R15's affect my milage considerably, on the '73 145?

No. As george already said the indications may vary slightly due to the tire being a different size. It's a bit bigger tire, so it has slightly more rolling resistance, but I wouldn't worry about it too much, in the end it's marginal. There would be more difference between driving with the windows open or closed.

Bram

They will affect your indicated mileage more than the actual,
in proportion to the ratio of the circumferences of the tires.
(Higher ratio = less engine revs but more torque)
In other words they will affect the speedo and odo readings more
than the actual miles per gallon.
--
George Downs Bartlesville, Oklahoma

So you are saying that the perceived mileage will change, but the actual work done will remain the same. Hmmm.

If I put shorter hands on the clock and reverse the polarity, will my car get newer?

Newness is all relative. Sodyou could also get a newer car and put its clock on 24 volt, thus running faster (humor me on that point). Then sit back while your car becomes relativley newer than the riged car >8^)