I admire your persistence and your never-ending curiosity on especially grammar issues Abla.

when I give another look at the issue I am led into a conclusion myself which is the possiblity of  "Arabic grammar marking "-an "

As you know Arabic forms adverbs by adding the indefinite accusative ending ´-an´ to the root. After this clue by remembering the adverbs answer questions such as how?, in what way?, when?, where?, and to what extent?.

Misal + en --> as an example

Misalen = misal olarak

Misalen ben soğuk bir ülkede yaşıyorum. ---> As an example [For example] I am living in a cold country.

How I am living in a cold country ? --> by imagining it. [by exampling it, by supposing it]

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temsil + en --> by representing ,by symbolizing, in a sybolized way.

                        how                   how             in what way

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temsilen yürüdüler ---> they walked by representing [something,somebody]

                                they walked by simulating [it ]..

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therefore I go for the idea of " some arabic origin words are altered into adverb forms by taking "arabic adverbial marking -an to their root"

Yes, but they confusingly look like Turkish participles. I guess if they really were participles this would be a productive structure, i.e. you could take any first part of a compound verb and make it into a participle. And it doesn´t work this way. So nice you understood what I ment, tunci.

Some call it pain in the neck.