You can break needles if you pull the fabric from one side. This bends the needle slightly. The tip of the needle then hits the support plate and ‘ping’.
If the fabric skews in a seam, it is because it is not restricted enough. You need to hold the fabric with two hands, front and back, and to let your hands ‘float’ while maintaining good tension along the seam. Takes some practice – on scrap bits of fabric.
Sewing heavy material is another matter. Your machine may not have the drive or torque needed to push the needle through. Just getting the needle moving may also be hard. You can push the needle through a very heavy spot by cranking the wheel on the right by hand. That works fine for a few stitches, but gets a bit tiring over any length.
In an extreme case the needle might not be strong enough. In that case you need to use a heavier needle. These are available in any sewing shop, and mostly they all have the same fitting. Take a current needle with you to check. I use needles from #60 (light) to #100 gauge (leather), and do have heavier.
For heavy canvas and webbing you may need a heavier machine. The gold standard for this is an OLD black Singer, straight stitch and no zigzag. I sew canvas and leather with it, but can also sew light silk with it. A wonderful machine.
If you are going to sew heavy stuff, you will need a heavier thread. Ordinary domestic thread will not be strong enough. The gold standard here is what is called ‘bonded nylon’ thread. This is better than ‘button thread’. Your shop may have to get it in for you. It is what I use on canvas and leather.
Cheers