Generally, the units used to count lectures or classes in schools are 時間, 時限, 限, and 講.
- N時間目: Used mainly in elementary schools or informal conversations. Although a single class may be 45 minutes or 80 minutes long, the term 時間 is commonly used without issue (as long as 目 is attached).
- N時限(目): Used mainly in higher education.
- N限: Primarily used colloquially by university students.
- 第N講: Sometimes used in serious, lecture-style textbooks in place of 第N章.
第N時 is rare in both spoken and written Japanese. It appears to be used in the same way as 第N講, but it's not a nationally shared practice. 第N時 could be a custom specific to certain universities, but I'm not sure.
第N期 is basically "N-th season", which is far larger than above. 第N期 is used for events that repeat in cycles of at least two weeks, or as long as a year.
Is a period in Japanese primary school a full hour
-- Normally it's 45 minutes.