With you overall, but given the toxicity of the fumes some quality / rated fume extraction might be the one area where cheap/self made item isn't worth it
If you're doing it a lot, then it's definitely worth making sure it works properly. If you're doing it occasionally, just make sure the area is well ventilated and you're not outright inhaling the fumes coming off the solder, and it's not likely to make any real difference to the health of your lungs.
Understatement.
I'd love agree with you... Unfortunately I bought some <50 bucks solder fume extractors and I'm pretty confident to say they don't work reliably.
They also contain a 120mm fans, a carbon filter and NO way to lead the fumes out oft the window.
However, you may be right that professional tools are the better choice in this case