1) Some aged people tend to regret having been lazy in their college days.
2) Some aged people tend to regret being lazy in their college days.
Both 1) and 2) are correct, and very close in meaning.
1) is very accurate in that it means at the time when the aged people regret their past – say, in March, 2004 – they are referring to actions that clearly happened at a past time, say in the 1950s.
2) is also clear because of the context – in their college days is obviously long ago, before the people were aged. However, the differentiation between the time of regretting and what they were regretting is less clear based on just the construction. For example, if you said: "I regret being so indifferent to Aunt Mathilde." it would not be obvious if you are being indifferent to her now, or if you are speaking of a past time.
In your sentences about selling the farm, the first three are fine. "I regret having sold the farm" makes it clearer that selling the farm was at some time in the past. "I HAVE ALWAYS REGRETTED having sold the farm" is not natural. "Having sold the farm" would have happened at a time before the point of speaking, yet the present perfect tense leaves one wondering about when you started regretting and when you actually sold the farm.
These sentences below from Google are correct:
I regret having quit'. HT Correspondent (New Delhi, October 25).
Farooq Abdullah on Friday said would like to shift to politics ...
We, too, regret having seen "Journeys with George".
Why I Regret Having Written This Book.
These sentences could also be written using the simple gerund: "I regret quitting," "We, too, regret seeing...," and "Why I regret writing this book." The sentences would be clear in this way, even without the careful distinction in time that the past gerund expresses.