I would say I could've gotten up early yesterday. The sentence "I could get up yesterday" doesn't make sense, since "could" cannot indicate the past. This could only indicate the present or future unless it becomes reflexive "It could have been so" or in your example "I could have gotten up early yesterday". "I could have (could've) "get" up early yesterday" also does not work. "Get" would have to be converted to gotten. I feel you may want to use your example in the sentence "I could get up yesterday, but I didn't". I don't want to explain to you how this incorrect phrase is almost correct but rather just advise you to not use it. In this case there are many who are guilty of using this phrase but it is not fluent English, just lazy English. Americans speak two languages. English and Bad English.

Here is a very interesting discussion that I also find really helpful: https://english.stackexchange.com/questions/122310/was-able-to-vs-could

No 2 is not possible 'could' suggests a possibility in the future and yesterday is in the past it has already happened so it makes no sense. You could use could in the conditional past. I could have gotten up early yesterday if the alarm had worked.