I would say suburbs are outskirts, yes. Also we say "in the suburbs" but "on the outskirts".
Not necessarily, some outskirts are rural areas not suburbs.
In English, we say "on the outskirts," not "at the outskirts."
How about "on the edge of the capital" ? I think in English this is said often as well - with the same meaning.
I am English and just answered edge, knowing what the periphery is as it is also a word in English!
Seriously, why isn't "periphery" accepted?
Likewise for me. Duo did not accept "on the edge" as meaning the same as "at the periphery" but most English speakers would beg to differ.
"Just outside the capital"?
"at the periphery" should be accepted too