When I need to match points, I glue pin using Elmer's white washable school glue. Here's how:
I go to my ironing board and place a pin through the points that need to match. Once I am satisfied with the pin, I make the pin go straight up and down into the mat as much as possible. This makes sure the points are matched up. I then place a tiny dot or two of Elmer's glue in the seam allowance next to the pin and use my iron on that seam allowance for a few seconds to dry the glue. Repeat for each point.
Now, when I take the pieces to the sewing machine, I have glue instead of pins holding the points together. If there is excess fabric between the "pins", I can ease that in as necessary.
If there are points, I sew with the point-side up so I can see where the seam intersection is. If there are points on both sides of the pieces, I will sometimes sew through one point, remove from sewing machine, flip the pieces over, and sew from the other side.
To increase cutting accuracy, it's a good idea to starch the fabric before cutting. Starch stabilizes the fabric so you get more accurate cuts. Starch also helps with bias edges, as it stabilizes the fabric so the bias edge is less likely to distort as you sew. You can use heavier starches, but even spray starch is enough to help with this step.