The problem with loading modern film in a IIIf seems to be the film catching on the pressure plate or film gate. To avoid this without cutting the film for a longer tounge, first attach the film to the take-up spool. Insert two business cards fully in the camera bottom, and slide cartridge and spool into the camera with the film between the cards. The cards will guide the film past the pressure plate and film gate. Remove the cards and wind the film a bit to see if the sprocket engages the film sprocket holes. If so, close the bottom and take up the slack in the rewind knob. The rewind knob should turn when you advance the film, like your Pentax. With practice this isn't as hard as it sounds. I've done it while driving a car on a rush job. If I was still using a IIIf I'd use a couple pieces of sheet film instead of business cards.
There are many fine lenses available for the IIIf, should repairs to your lens be too expensive. I've used one Summicron for maybe 35 years. One of the sharpest lenses I ever tested in a quick and crude, but critical, test was the 50mm f/2.8 Elmar. The 50mm f/3.5 Elmar was well regarded in its day, but those two faster lenses were better. The f/3.5 Elmar does make the IIIf easy to carry in a pocket, and the f/2.8 Elmar isn't much thicker. I've also used Canon and Nikkor lenses. Most were good for their time.
I second the recommendation to get Morgan & Lester's Leica Manual, 12th or later edition. The major online book resellers and perhaps ebay should have copies. There were several Leica manuals by other authors, but the Morgan & Lester book may be the best.