Hello,

Adsorption is due on the electrostatic forces between charges on the carbon surface and ionic methylene blue.

Depends on the type of adsorbent.

I agree with comments on charges and depends on absorbent. I have attached info link on methylene blue - a Synthetic dye with some medical uses. https://en.m.wikipedia.org/wiki/Methylene_blue

Is it organic? As we try to understand concepts, we all want to understand complex truths, but need to remember to avoid jumping to conclusions or generalizing until a substantial amount of data and literature are collected. Probably most of us have done it a few times. As more data and information is accumulated, you may find the theory fits in some circumstances, cannot be proven or has exceptions.

Some things are more hydrophilic, others are more hydrophobic,  so in some transport media like water, thing transport to the substrate they are most like.  Thus some compounds stay in the water or concentrate at hydrophobic sites. Impossible to understand this without adding chemistry:  the identical chemical structure can be hydrophilic and hydrophobic by only changing pH.   Can almost always create an experiment in which 50% stays in solution and 50%  is absorbed onto a surface phase. 

Organic compounds are not always adsorbed with high efficiency than inorganic metal ions. To see this, you should express q values in mmol / g units, and then to compare.

Yes, I concur.   Inorganic metal ions surface area is often rather small so they likely take up little surface area of a substrate.  The technical difficulty is that once they are on the surface, the surface charge will often invert decreasing adsorption efficiency.   Interestingly,  organic compounds seems to innately orient themselves into a hydrophilic surface and the other half is hydrophobic.  Thus either half could bind to a substrate depending upon the structure of each.

In my opinion the reason is for this: base of the activated carbon and methylen blue, both have carbon atomes and in aquoa phase both of them are hydrocarbon ... So activated carbon can adsorb hydrocarbon' s oposite poles better than inorganic molecules..

The physico-chemical phenomena involved with inorganic and organic molecule are fundamentally different:

To simplify them:

Inorganic: ionic forces long distance strong forces, to separate/filtrate them you would use techniques like ion exchange chromatography. There won’t be adsorbtion but exchange of ions. Altenatively, you may use chelating and/or precipitation techniques to remove some inorganic ions.

Organic: mainly short distance, surface, weak Vander Waals forces, you could utilize high surface area particles (activated carbon, precipitated or fumed silica with various surface modification, clays, nanoparticles,…), with polar affinity for the organic molecules you’re seeking to adsorb. Some may have ionic groups but a lot of them do not. Therefore you’ll utilize liquid chromatography techniques to adsorb them. Alternatively or concurrently, you could utilize variation of solubility to separate organic molecule.

The efficiency of these separation processes will depend on the composition, concentration, temperature,…, of solute and the solvent utilized.