Yes, there is no problem with those combinations. As far as your specific examples are concerned, "I should have slept earlier" is kind of odd (probably you mean "I should have gone to bed earlier"), and "I would have studied English harder when I was a student" feels a bit incomplete without some context to provide an "if..." or "but..." aspect.
The third conditional relates to an untrue condition in the past. All adverbs telling us when in the past are possible.
If I had started studying English when I was a child, I would be a fluent speaker now. If she had gone to bed at a decent hour last night, she would not be yawning this afternoon. If the army had built a high defensive wall five years ago, the city would not have