My answer 'The platform of the train station is full of people' should be accepted in my opinion, as it sounds quite natural in English.
In the train station, not of. Of the train station doesn't sound natural at all.
British speakers are likely to use
railway station rather than "train station" here
or just "station"
The platform at the train station is full of people. --- wow! this is an awkward sentence... the way to say it in american english is the train platform is full of people.
"The platform at the train station is full of peeps" was not accepted.
I can hear him say "be-takhanat". Should he not say "ba-takhanat" since it's a definite noun.
No, because in the construct state (only) the second noun takes the definite article.