1969 Other Ford Models F-100 Starting problems

First of all my battery would begin to drain overnight and the engine would not even begin to crank in the morning. Not knowing what my problem was I installed a new starter and new selenoid since they were relativly cheap. I then had my battery tested and it is good since it also is only a few months old. After I installed all the new parts I went to install my battery last and as soon as I touched the battery to the cables the engine began to crank with the ignition in the off position. I was able to start the engine but I had to disconnect the battery cables in order to shut the engine off. Before I installed the new parts this was not a problem. Also my new starter seemed to be grinding on the flywheel even though I made sure to install it securly. Is there any way to tell how to exactly line up the splines when you are installing a starter? And how do I figure out why my engine cranks with the key off?