I'm not sure exactly what certain bits mean specifically, but:
Visit program [this sounds fine, although Visit Program - with both words capitalised - is better as a title. There is probably a better title to use but I can't think of the appropriate wording just now]
State zoological park of Udmurtia [again with capitals because it is a title - State Zoological Park of Udmurtia]
June 26, 2015 [fine as it is]
8.30 – 9.00 Breakfast. [I would put a colon in there, and after all following times below, e.g. 8.30 - 9.00: Breakfast. The full stop is not necessary, but there is nothing wrong with having it there]
9.00 Appointment, meeting with heads of departments. [I would leave out the word appointment, but there's nothing wrong with having it there]
9.30 Work in zoo. [I'm not sure what this refers to?]
10.30 Domestic animals (animals') department, ornithology department. [Domestic animals department - the apostrophe is not required. Should this and the following examples say "Work in zoo" in front of them? And should the example above say something after "work in zoo"?]
11.30 “White North” department: walruses, fur seals, polar bears. [fine as it is]
13.00 – 13.30 Lunch. [fine as it is]
13.30 – 14.00 Work with press. ( “Work with the pressmen”,“Work with media”?) [I would put "Work with the media" or maybe something like "Public relations with the media" might be more useful as a phrase?]
14.00 – 15.30 Work in zoo. Felids department, wolves and bears department, primates department. [fine as it is]
15.30 – 16.00 Dinner. [fine as it is]
16.20 Passage to railway station. [not "passage"; maybe "transfer"? If transport to the station is provided (e.g. by car or taxi), then "transfer" is appropriate]