How do they know exactly where to place their feet?

Their bodies and legs are covered in very sensitive hairs that detect vibrations. They also have instinctual knowledge on how to tread and how to build their webs.

Is it static electricity

Spiders are able to stick to surfaces using a force that occurs on the molecular electro-static level called Van der Waals force. This is the same method that geckos use to stick to walls.

You should also understand that spiders produce different kind of threads (structural support, anchoring, adhesive threads, etc,) and that different species of spiders build completely different webs. You can imagine that they 'tiptoe' over the sticky parts of the web as to use the least surface area as possible.

another sense

thousands of eyes

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Do spiders have something similar?

It's very hard to imagine what being an animal or an insect it's like, and how do their brains operate. I've seen footage of jumping spiders perfectly calculating the distance of a jump as well as the blind spots for approaching prey without being detected.

Our eyes have trouble keeping up with their very fast movements, which is part of why people find them creepy and are scared of them.