"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?
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"
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 think your comments and those above just made a light come on. In English when we say 'on the bus', we mean riding in the bus. So 在 is just the location and 里 is implying riding (inside the subway car).
Is it ungrammatical in Chinese to not provide an object for the verb 吃? Should my failed attempt "在地铁里我们不准吃" also be acceptable?
It is still grammatical. I think there is no strict rule in Mandarin that a verb is transitive or intransitive. An object is added when the context requires it.
We do usually need an object for 吃, but when the object is understood, we can omit it.
Well, to me 吃饭 is more like a meal and doesn't encompass like snacks for instance.
Why isn't 不可以 accepted as a translation of "not allowed to" when they told us in a previous lesson that 可以 is supposed to be used when permission is in question?
可以 gives the idea of you may not. 不准 is stronger and gives the idea that you are not allowed to. I guess it shows the level of sternness in the situation
So can the words order here is 我们不准/不可以吃东西在地铁里？ Do we always need to place the location phrase at the first of the sentence?
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.
I got this write however I thought that "东西" means "things" so why is the word "things" not included in the answer. (I realise it doesn't sound natural in English.)
It is true that 东西 means "things", which is used generally in this sentence. If you include 东西 in the sentence, then you are saying "We are not allowed to eat anything on the subway", where anything is implied by 东西
This is a common sentence said in Chinese.
Going forward you will find that there are other word choices in Chinese that would allow you to say Eat without Things (in this example 在地铁里我们不准进食). It is fair for Duo to keep things simple to be learnable.
See Keith_APP's answer to pat5120 above. It helped me understand the placement of the 'where' component. I found a rule that helps in general: Subject, when, where, how, action