How dangerous are the solder fumes? I've heard that there are now lead-free "solder wires", should we switch to them? (unfortunately that doesn't help when unsoldering old equipment)
Probably the average politically correct Health and Safety moron would tell you that the lead in solder is extremely dangerous.
I have been soldering my own projects for well over 30 years now and my brain damage is only marginal. So marginal that it is not near damaged enough to be able to get a job in Health & Safety. For that you have to have almost no brain at all.
To be on the safe side when soldering using lead solder do not put your nose directly over the fumes and breathe in heavily. Just use common sense. You will probably do many things each day that are far more dangerous.
Unless you intend to spend 24 hours a day soldering in a confined space I would not worry about it. Some idiot with a cigarette sitting next to will cause you far more harm.