Should "They take the bridge", in the sense of "Take the new road!" be accepted here? I haven't reported it yet since I'm not sure that one can use "tóg" in this sense, but it feels correct.
Take should be accepted. There are many contexts in which it makes sense.
Not really: although "tóg" can mean either, in this case it would almost certainly be used in the sense of "build". "Tiomáineann siad thar/ar" would be a better way of expressing your meaning.
Am I the only one whi pictured Gandalf reading from the Dwarven book in the mines if Moria?
Tógann said does mean "they take", and if the sentence was Tógann said an t-úll, then "They take the apple" would be the most sensible translation. But the course contributors want you to understand that if you want to say "They build the bridge", then the Irish is Tógann siad an droichead.
The sense of "They take the bridge" meaning "they go by way of the bridge" is probably béarlachas, but you will hear Tógann siad an droichead used in that way. Just be aware that that isn't always what tógann means, and, in the case of something like a bridge, the "build/construct" meaning has to be considered.
Yes, Tógann siad an droichead with the intended meaning of “They go by way of the bridge” would be an overly literal translation from English — Téann siad ar an droichead would be preferable for that meaning.