I don't think in English we'd say 'on the east,' rather 'in the east'.
I think that is probably regional, but I was surprised to see that "in", which is also more likely to my Polish ear, wasn't accepted. Added now.
What's the difference between okolica and obszar?
"Okolica" = "obszar" around something, your house for example. If you live in a city, "okolica" can refer to "neighborhood".
In most cases, there isn't one, although obszar is a more universal word. It may be used in some contexts where okolica would not sound well. The general meaning is also slightly different.
Why can't I say "Ten obszar jest we wschodzie" instead of "na wschodzie"?
As native I can say that " we wschodzie" sounds for me like "inside the east". We just don't speak like that.
I said "ten region", but it didn't accept it. I thought "region" and "obszar" were similar enough.
I think region is a geography word, and obszar is just some area that can include whole Russia, and can also include just my night table's surface...