Hi Anna, for the most part, your sentences are good.
1. He has studied English hard and his language skills are better now.
2. I haven't finished my work yet and I cannot go out (now).
The “(now)” isn’t necessary here, but it does place emphasis on the idea that you cannot go out now.
3. We were late and the grocery is closed.
Remember that the present perfect refers to actions that began in the past and continue in the present.
1. I met my old friend on the street (in anytime in my life)
2. She studied English, Russian and Ukrainian at school (a long time ago)
3. I worked in the Department of culture
I hope this helps!