My experience about the hazards of both:
Battery acid is not nearly as dangerous as people sometimes make it. OK, so it's not healthy either (and for gods sake, don't get it in your eyes), but... the first time I had to buy a battery for my old car I went to the nearest supermarket and found a neat stack of them. I found one that looked promising, but unfortunately I couldn't find a price for it. So I thought that maybe it was on the bottom and turned the battery upside down. That's when I learned the difference between "spill-proof" and "hermetically sealed". I splashed some on my hands, sweater and the new pair of jeans I had bought the previous day. I went off to the bathroom (alerting a store worker on my way there) and washed off my hands with plenty of water and panic. Incidentally that also made my jumper sleeves a bit wet. However later there was no effect on either my skin or my sweater. My jeans however had attained a unique pattern of tiny holes the next day. :P
So basically - yes, the sulfuric acid in the batteries is a hazard, but even if you get some on you - don't panic and just wash it off with plenty of water (especially from the clothing). It won't harm you unless you let it soak for a while (well, except maybe if you get it in your eyes or something). If you even wear simple household rubber gloves, you'll be more than adequately protected.
Rust itself however is no hazard at all, even if it was caused by the acid. And it can be caused by other reasons too (like water).
Headlights - most headlights (and all the various other light bulbs of a car) can be changed quite easily (provided you can
get to them), but there are two things to keep in mind:
- For the headlight bulb (but not for other, less powerful bulbs), don't touch the glass with your fingers. It's also stated on the box. Hold the bulb by it's metal base. The bulb runs very hot (unless it's one of them fancy LED bulbs) and the grease from your fingers will make it hotter, thus shortening it's life.
- If it's a xenon bulb (it has that distinct blue color), don't change it yourself. There should also be a warning sticker in the car that the bulb uses very high voltages (mine says something about 25,000 volts), so if you touch that, you'll really harm yourself. I don't know if this applies only when the bulb is on, or if there is any residual charge in some capacitors, but the general wisdom is - xenon bulbs need to be changed in a special workshop and cannot be serviced by owners themselves. Everything else thought is doable.