"We are not allowed to eat on the subway."
If '在地铁' means 'on the subway', why do you have to add 里？
Also in this example the characters for 'on the subway' were first, in a previous quiz example the characters were last. Both English phrases mention 'subway' last. How do you determine when to the place the object (subway) first?
In English we have different prepositions to indicate spatial relationship: in, on, at, over, above, under, beside, behind... in Chinese, mostly we say 在 for all these. Imagine that we can't insert 里 etc. here. We won't be able to precisely deliver such spatial concepts.
Sometimes we need to have words like 里 here (里, 外, 上, 下, 旁, etc.) to be natural. Nonetheless, it is not absolutely required in all cases. e.g. both 我在地铁站 and 我在地铁站里 are correct. Both tells people about your location, only the latter tells it more precisely.
I could be wrong, but I think they mean the entire subway. Like the stations and all. So they're saying they can't eat in the subway station. So that's the only explanation I can figure. But yes, not enough context to determine. If they were on the train though, I'd say either "地铁上" or "车上"
It word order depend on the verb.
A simple way to have good word order is:
A place at which the action happens : in front
A place on which the action exercises : after
For 吃 to eat we definitely can't exert this action to a place (as we only eat food not location), so putting the location afterwards is not viable.
But if the verb is 坐 to sit, it would be viable both ways.