When weaving I use fabric strips, pins, and a 1/2 inch foam board. If I know the dimensions I am working towards, I will cut a piece of lightweight fusible interfacing in those dimensions and pin that to the board first, bumpy side up. I also use the tjaye flat weaving needle.
Also pictured is a bias tape maker. I have a one inch and a half inch, however I often prefer to just use my fingers to roll the sides of the fabric towards the middle while I press with the iron on the highest steam setting. I have had few issues with heat, but you may prefer to use a tape maker.