I wouldn't take my Lo with a cold, just to avoid spreading it to others and making it linger longer in Lo's system. Take the week off, give Lo lots of cuddles and get a bit of fresh air. Hope Lo's cold improves quickly!!
I wouldn't take my baby swimming if she/he has a cold because germs can spread and my baby could get worse from the water. I would wait till the cold passes.
I wouldn't but I have a major fear of it going onto his chest and him getting really sick, possibly a mild obsession as it's never actually happened!