You can't digest chewing gum, but it doesn't actually seem to do any harm if you swallow it. This is based only on anecdotal evidence, though (having swallowed lots of chewing gum over the years & being Not Dead). No idea about Blu-Tak, but I think I managed to avoid swallowing that... it was pretty vile, though.

The alginate, apparently, sets faster depending on how you mix it -- if you use colder water it'll take longer to set, and presumably (as with most things like this) the amount of water used makes a difference as well.