Learn English – “I haven’t seen you the whole year” vs “for the whole year”

TRomano makes a good point in his comment: Many of these could appear in different contexts. It's hard to say whether these are "correct" or "incorrect," because there are many different scenarios in which they may appear. That being said, I've tried to answer based on what I believe to be the implied context

In the given context, "all life" is incorrect. (1a)

Likewise, "all time" (2a) is incorrect, but you will see the phrase "all time" appear in instances like:

Beyoncé had one of the best videos of all time.

Babe Ruth is considered to be one of the all time greats in the sport of baseball.

For the third round, "all day" (3a) is, in fact, correct. However, I would argue that both "all the day" and "all of the day" are incorrect. I have never heard either used in American English, and to a native speaker they would certainly be seen as incorrect.

I've been working all day!

For the fourth series, the same applies as the third. 4a is certainly correct, but 4b and 4c will never be heard (again, at least in American English).

She has been out shopping all morning!

There is a slight, but meaningful, difference.

"Once a [time period]" implies frequency observed over a range of time greater than [time period]. "Once in a [time period]" implies an observed frequency of 1 in a single [time period].

If somebody were to say something occurred once in a month then he means he is talking about an event with a time of a month. If someone says something occurs once a month then he definitely has data larger than a month.

Example:

My last boyfriend, Eric, would buy me flowers once a month! But John has only bought me flowers once in a year. Does John hate me or is he just less sentimental and thus will only buy flowers for year anniversaries?

Another example:

During the first year of our relationship, Phillip bought me flowers once a month. Why would he now only buy me flowers once in a year?

As FumbleFingers brings up in the comments, the "once in a [time period]" could instead be an application of figurative speech and not based on technical data. The following example shows a usage of the phrase that indicates exaggerated speech is at play.

Wow! That's rare; it only happens once in a blue moon!

This is perhaps more indicative of a common idiom but still important to bring up.

To slightly elaborate on what was established above, it may not be obvious that the phrase "once in a [time period]" can be used to establish a cap on repetitions in a [time period]. See below.

Alice: "So, he goes to Mexico 10 times a year?"

Bob: "Yes, but never twice in the same month; he only goes once in a month."