These two versions of how to recite Al Asr, are different...

format_quote Originally Posted by crimsontide06

the guy just says "wal as" I think, I really cannot hear it good.
In the first video the guy says "Asul".

As brother Huzaifah said above, both of them are reciting "Wal 'Asr" but in the first video, the sound of 'r' at the end is not audible properly. The second one is more clear.

format_quote Originally Posted by crimsontide06

In a booklet I have it is spelled "Asri"

In the 2nd Aya, my booklet says "Khus-rin" but neither video says "rin"

When the Ayah is written, it is written with all the vowel signs. That is because sometimes you can join one ayah with the next one while reciting and the last vowel helps you in joining it.

For example,
When a person stops at "Wal 'Asr", he simply recites it like it is recited in the video above.
But when he wants to join the first two verses, he will have to recite it like this: "Wal 'Asri Innal insaana lafi khusr", that is without breaking his breath while reciting. Like the audio here:

Similarly, if he wants to join the second and third Ayah then he won't stop at "lafi khusr", he will continue and join with the next by reciting "... lafi khus-rin illal-lazeena aamanoo ..." until the end of the ayah.

format_quote Originally Posted by crimsontide06

Also, is the stretching out or sounds, required? Which is done in the 1st video.

Stretching the sound is part of Tajweed. It is highly recommended, but if you are a beginner, then you can start with the correct pronunciation first and then study the tajweed details.

Thank you both!