Iron and rust

Does rust spread?

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In the sense that if there's some it will grow (like an organism), no. We just call it growing because it looks sort of like that.

In the sense that rust helps moisture and oxygen reach surface right next to it - because rust shifts things around and is itself porous[1]. (...that said, rust, like any oxide layer, can slow down and potentially even stop oxidation from going deeper. This tends to work better in some other metals (liku aluminium) than in iron, though)

Technically, rust starts at nucleation sites, so you have places where it forms earlier than others, which means that even unprotected iron won't rust uniformly, and you can be forgiven thinking it's spreading from those sites.

And that effect looks even clearer when that iron is largely protected (paint, zinc coating, chrome or nickel plating, etc.) but some of that protection breaks (paint is the best example because it's softer and more brittle than the others just mentioned), it will spread from that side because that break increases makes both oxygen and moisture avaiable there. If it had no protection it would be relatively uniform.

One of the reason you are supposed to oil cast iron pans is that it won't rust as easily - the oil will block moisture and oxygen by just being there.

Is rust bad for you

Short answer:

iron oxide itself is not harmful

but it happens most in moist places, which also breeds things that are harmful

For example, a a rusty water cooker is no risk, because it's purely rust, and the frequent boiling will kill most anything.

(An iron / cast iron pan will sometimes be doing chemistry, which can matter, but barely so if you clean it well and/or use it frequently. )

Rusty nails and surfaces can be bad, but this is because places that collect rust are typically also dirty and moist, which is a good place for bacteria to grow to large numbers.

Bacterial spores such as those causing tetanus will take better on rough surfaces with dirt and moisture around - which happens to include rusty nails. (verify)

So stepping on a rusty nail in an old dirty moist run-down industrial building is a little riskier (and perhaps more likely) than stepping on a rusty nail in your room.

A wound bleeding will will wash things away - that's part of the point of bleeding. That said, e.g. tetanus is easier to prevent than to cure. At least try to catch it early - stiffness of the jaw and neck are early indicators.