http://www.youtube.com/watch?v=5Wdztx02rZQ
This is because of a rectification (It is operated by a magnetic ballast with a glow starter).
One end is clear, the other have a heavy blackening.

Unfortunately this seems to be a common problem with T5 8w tubes on magnetic ballasts. Particularly because a widespread application of these lamps is in 24/7 maintained emergency lights in public buildings, where they need frequent replacement.

But if they operates 24/7, there are no ignitions and therefore their life should be prolonged.
But i think this is one of the reasons why we needs to replace the T5 8W lamps every few months in the instant start electronic ballasted fixture at the bathroom of my mother home.

Count operating hours: If it is burned 24/7, it reaches the 8000hour life rating in less then one year of operation. The rated service life (so when they are supposed to be replaced) is 4500hours, what mean with 24/7 use the lamp should be replaced twice a year.
I would not expect more from such small lamps...

Why the argon buffered miniature T5s of 4-13W have a shorter lamp life then the larger T5 HO/HE, T8 (Both argon and krypton buffered) and T12 fluorescent lamps?

Why the argon buffered miniature T5s of 4-13W have a shorter lamp life then the larger T5 HO/HE, T8 (Both argon and krypton buffered) and T12 fluorescent lamps?

Simply because they are thoroughly different lamp designs, beside using the same tube diameter and sockets.
At first, 4..13W are of very old design and in fact no really invest into their future development. Coating them with tri-phosphor and/or high CRI mixtures was the first improvement on these lamps after few decades and i guess it will remain the last one, as it is the only feasible to make without having to fully redesign the lamp (the discharge remain untouched). That mean, then recent advancements in electrode materials and technologies didn't reach these lamps, as their use would require significant engineering design work and this cost a lot of money.
Other reasons are more technical:
On so short lamps you e.g. can not play with electrode shape to make them more robust . Compare the "dead length" (the part of the tube that does not generate light) of modern T5HO lamps with the overall length of these old T5's and you will find, then still on 8watter there will remain no room for the glowing part...
Krypton buffer gas stress electrodes way less then argon due to it's heavier atoms, however the plain use of krypton would lower the arc voltage, thus requiring narrower tube to bring the voltage back up (the reason, why T12 became T8, when switched to krypton based fill).
And generally, low wattage discharges are generally way less efficient, but nearly of the same manufacturing costs then their higher wattage models, that make their use economically not competitive against other technologies, recently mainly LED.

Is the argon buffered T8s (Such as 15W, 30W and 50W) also suffers from such short life?
The actinic UVA 20W T8s in our bug zappers in my hostel i live (Which i think also argon buffered), didn't last so long, despite they are also operated 24/7 on a preheat magnetic ballast for two 20W T8s with glow starters.

Is the argon buffered T8s (Such as 15W, 30W and 50W) also suffers from such short life?
The actinic UVA 20W T8s in our bug zappers in my hostel i live (Which i think also argon buffered), didn't last so long, despite they are also operated 24/7 on a preheat magnetic ballast for two 20W T8s with glow starters.

It may and may not, it depend, how particular model is designed, what was the top priority, etc.
There are many contributors for long or short life, the only argon vs krypton fill is only one of them, other is the exact electrode shape or use of the electrode guard, but there are still many others (the complexity and cost being one of them too).
Electrode guards do help in argon lamps, but usually require more "dead" space (what finally does not light) to accommodate them, what make these tricks unusable in physically small lamps, as their efficacy would suffer too much.
Remember, then these things are frequently matter of compromise, so lamps with the same designation might differ between different manufacturers, as one might prefer lamp life over efficacy (so use these guards, so reduce effective glowing length, so efficacy...) and another prefer the efficacy, so use the assembly, that eat up as little space as possible to have the glowing part as longest as possible.
With longer lamps this compromise is much easier, as the extra space occupied by advanced electrodes is not as big part of the long lamp, so does not cause so significant efficacy loss, so will be used more likely.

And UV lamps (all) are of special kind, as they usually suffer from useful output degradation, what cause at the end, then their primary end-of-life limit is insufficient output, what happen earlier then electrode failures, so these lamps are frequently more optimized for the efficiency.
But very frequently these use exactly the same discharge design with lamps for general lighting produced by the same factory, as any difference from standard (general lighting production) cost a lot, as it cannot share components and/or machinery. So each such difference should be justified, if it is really necessary for the purpose of the lamp.