This is the guitar. It has no pins on the bridge. Does that mean it will work if I put nylon strings on it instead of steel strings?
Guitars that are made to use steel core strings (bronze or nickel wound) are made differently than guitars made for nylon (or gut) strings. The steel string guitars have a different and stiffer bracing made to hold the higher tension of the steel strings.
If you try to put nylon strings on a steel string guitar, your action will likely be too low and the strings will not play well. The nut slots of your guitar will also not match the gauges of the nylon strings and you may have an issue with the thick high nylon strings not sitting in the slots for thin steel strings.
If you want a softer playing action closer to nylon strings, there are a few manufacturers that make a "nylon like" string made for steel string guitars. One example is the "Silk and Steel" set from D'Addario, which has a softer feel and a warmer sound than standard steel sets.
If you do want to try the nylon strings, you can tie a barrel knot or other thick knot in the end of the strings in the place of the ball.
Because of the construction of the guitar for higher tension steel strings, your tone and volume will be lesser with the nylon strings if you do get the action and nut gauge difference sorted out.
You need to do knots. My personal preference is two knots on the lower strings and three on the higher strings
Besides that, are you really trying to put nylon strings on a steel stringed guitar? Different instruments are designed for different neck tension, and you might even damage your guitar.