This sounds like a timing issue to me. The thread bunching up may be due to the hook not grabbing the thread or the take-up lever not taking up the slack at the correct time. If it's missing stitches in zig-zag mode then that would also be due to either hook timing or possibly needle bar alignment.
Simple things to check:
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Make sure that the needle is installed correctly, especially that it is oriented the right way and inserted all the way in
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Make sure that the take-up lever is threaded correctly
Assuming these are both correct, you can try the following:
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If possible, insert a fresh needle (at least, you will need a needle that is undamaged and not bent from the shank up to the eye)
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Remove the plate, leave the machine unthreaded
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On the straight stitch setting, turn the hand wheel slowly and check that the eye of the needle is exactly level with the hook as they pass each other (this should happen close to the bottom of the needle's stroke but may not be exactly at the bottom)
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On the widest zig-zag stitch setting, again turn the hand wheel slowly and check that the eye of the needle passes closely to the hook (it won't be exact because the needle has moved, but it should be just slightly early on one side and just slightly late on the other, not noticeably early or late on one side) and also check that the needle is not colliding with any solid parts of the machine on either side
If the eye and the hook are not aligned as they pass each other, then you have either a timing or a needle height alignment issue. If they pass correctly on the straight stitch but the needle is noticeably early or late on one side of the zig-zag stitch (and fine on the other side) then you have an issue with the horizontal alignment of the zig-zag stitch.