To begin with, the noun rank has nothing to do with the adjective rank.
The noun is of French origin (possibly Frankish ultimately) and originally denoted a series or line of things (range has the same origin); then specifically a line of warriors or soldiers (whence our 'rank and file'); then the successive lines, the first, second, third ranks, and so forth, in which soldiers are deployed; and finally, by way of one's position in the front, middle or rear rank, one's grade or standing.
The adjective rank is of Germanic origin; the precise line of descent is obscure but it seems originally to have denoted various attributes of the noble warrior: proud, haughty, rebellious, strong, vigorous, full-grown. In ME the martial connection faded and the word became used particularly of undesired and excessive strength, vigor and abundance; it was extended to vegetation (we still speak of 'rank weeds') and to loathsome behavior and smells (O mine offense is rank says Claudius); eventually it acquired such a strong negative connotation that came to mean 'corrupt, foul, festering', and eventually simply 'extremely (offensive)'.
See the Oxford English Dictionary, 1st edition.
When your source writes of rank dishonesty it probably does not intend any one of these later senses but (at some level) all of them simultaneously: extremely gross, corrupt, loathsome dishonesty.
According to the Cambridge Dictionary, the expression "better you than me" has this definition:
said by someone who does not want to do the thing that someone else is doing
This is a mainly US expression: the UK equivalent is "rather your than me". This fits with the first definition that you quote, but not the second. I agree with the Cambridge Dictionary and your first definition: I think that the second definition is wrong.
A better expression for the second definition would be "I'm alright Jack"
Best Answer
Ages is used here as a colloquial term for "a long time". It's derived in this case from the meaning of "a distinct period in history", and it's used to indicate that there's no need to worry about the exact time. So, in your example:
...means that while a holiday is planned, it's a considerable time off, probably several months - long enough that it does not need to factor into your current planning. Similarly...
...means that you have plenty of time to do whatever it is you're talking about. In this context, that could mean several hours or several minutes; it's entirely context-dependent.