挺好！

I had to look up "clement" and "paeans", I'd never heard the latter and forgot the meaning of the former.  They're good words but rarely used.

Free as A Goose

"paean" might be better than "paeans" like as if there were one song of spring rather than many?  And actually I'm not even sure if "paeans" is used.  But I think only a latin teacher or a very serious english professor could tell you how to use that word.  Maybe you can find examples of its use in literature.  I don't know. 

This last sentence is a little awkward because "due to" seems to modify "nothing alleviated" which is the opposite of what you mean.  Either separate sentences or "nothing alleviated my lethargy, a lethargy due to the lack of sleep..." would be better.

It didn't fear of human. (I'm sure you know that this is a very literary usage "fear of human".  Normally its "fear humans") Instead we were astonished at its sudden and perculiarpeculiar intrusion. It just stood motionlessly where it had landed, as if glued to the ground, yet it looked like a king inspecting his territory solemnly, eyeing us all as pityiful, and ignorant, puny creatures.("pity" is the noun.  And remember the form for lists is "A, B, and C" although here I think its more literary to leave the last "and puny" "and" out, but some might disagree.)

Instead of heading straight to the teaching building I remained there and had minutes of eye contact with it. What a beautiful creature and what a gift in this delighting morning. (I think "delighting morning" is okay, but certainly "delightful morning" sounds more natural.  But "delighting morning" might be acceptable in a literary style, I'm not sure.)

As I was going to be late, I reluctantly moved backwards, still facing the goose, step by step in the direction of my classroom. When I ascended to the first floor, I took a glance at where it stood. Things got even more interesting. It was several steps away from its "invisible palace", still cool and prideful, but I could see three or four dama in our school uniform chasing it lumberlyawkwardly.(Or "full of pride".  I don't know what "dama" is, 用中文可以说吗？  But in this case its probably appropriate.  "lumberly" is a very rarely used word.  "lumber" is more commonly used.  "He lumbered towards the hospital."  Or of course as firewood, "He cut down some lumber for the fire."  However, I looked up "lumberly".  Most "-ly" words are adverbs, almost all of them.  "lumberly" is not, its an adjective.  This surprised me as well.  So you cannot use it here to modify "chasing".)

It was going to be caught! I held my breath for it. Somehow it finally sensed an atmosphere of tension and flapped several meters away uneasily, but this was already a considerable distance for its hunters, as running goes much slower then flying. The dama chuckled and kept sneaking near, so it cleverly flew up to a higher platform. (You could also say "sneaking nearer", "sneaking near" might suggest just "sneaking nearby" rather than sneaking closer to the goose.)

This time our dama felt rather impotent, but nothing frustrated their mind to catch the unexpected walking feast. One of them tried to reach clumsily to the goose. TheAt that instancet it flew vigilently up to the top of a tree, and the next second it soared into the sky handsomely, and finally left from where it had entered.("instance" means a particular example of something, or occurrence of something. "Instant" means the period of time.  "vigilantly" doesn't sound right here.  "vigilant" means watchful, so its a sense of "The vigilant night guard/watchman, never left his post once during the night."  So he was very watchful.  It doesn't sound right with leaving some place.)

What a soul of freedom. It goes (to) where it likes and has the ability to escape persecution and to leave when it likes. I've never seen a human being as free as this goose.

"nothing frustrated their mind to catch" is very awkward.  I think its okay grammar and it even gets across what you want to say, but its awkward enough to go beyond just being literary I think.  "nothing gave them pause in catching" "nothing gave them pause in pursuing" "nothing discouraged them in catching" "nothing discouraged them from catching"