Due to lack of explanation on google about how this specific type of ph meter works
In general - exactly the same way every other pH meter does. Many details at http://www.ph-meter.info
First of all,Is the part that marks with red arrow in the attached photo refer to the reference electrode?
Reference electrode is somewhere behind the junction, that's for sure, but where it is - no idea. Somewhere inside.
Does this type of ph meter also leak electrolyte(or something)into the tested solution during its operation?
A bit. Typical amounts are way too low to matter, unless you are dealing with some very specific, high purity solutions. But then, you shouldn't use a cheap pen pH meter.
Regard to the manual(second photo)"OPERATION"part 6-7 sections it says"after finished,clear with D/W and replace the cap".I understand that after i finish to make measurementand before i put it in storage,i need to stir/clean the electrode bulb in distilled water solution and replace the protective cap.But do i need to dry the glass electrode from distilled water residue with tissue(or something)before i replace the protective cap or after i stir/clean the glass electrode in distilled water solution i just replace the cap without touching or drying the electrode?
Don't dry the electrode. Actually leaving a bit of excess water should be a good idea.