Nat, is the custom of Easter basket still observed in Ukraine?
Absolutely. And also we have much larger baskets than the one on a picture :) We take the whole table to the church for blessing, quite literally :)
I think it was when today`s western Ukraine belonged to Poland?
I don't think Poland had more significant influence on the Ukrainian Easter celebrations than the other way around, because even though Ukrainian Catholic Church is Catholic, it is more like Greek Orthodox Church where it draws its roots from, than Polish Church of Roman rite. In addition, the Polish presence in western Ukraine was more city-bound and the villages lived what they knew since times unknown. This is what I like about my village - it keeps old, old traditions. Nowadays though, there are exchange of cultural traditions and it is Ok, bu I wish everyone kept one's uniqueness. It makes it more interesting.
I found this film but it was made in Ukrainian church in Ontario
It is nothing compared to an outside, rural setting somewhere in Ternopil region with ages-old traditions.
the priest came to the house to bless the food, usually before noon on Good Friday, or sometimes Thursday
It is impossible, you might have confused the dates. Priests will never bless food on Good Thursday or Friday. The reason is Christ according to the tradition was crucified on Thursday; Food blessing and the end of the Lent coincide with the Ressurection, which is three days later.