If hygroscopic compounds can absorb water vapor from air, can they also absorb liquid water from certain material( ex. water within a wet cloth or water within some other substances)?

Yes. Drying agents like [ce]MgSO_4[/ce] are often used to pull water out of other materials in industry or chemicals in the lab. The various active ingredients in under-arm deodorant are hygroscopic. [ce] AlCl_3 [/ce] used to be used in deodorants for its hygroscopic properties. It is still in use but is gradually being replaced by others that serve a similar function.

if they can absorb water vapor from air, weren't they react easily once expose to air?

 

and which hygroscopic compounds are most reactive(that can drawn most water out of a substance)?

I'm not sure what the "most" hygroscopic compound is. I'm not sure if anyone knows that. [ce] MgSO_4 [/ce] can absorb 12 moles of water per mole. So one gram of [ce] MgSO_4 [/ce] can absorb about 1.8 mL of water. [ce] CaCl_2 [/ce] is another common drying agent as far as simple salts go.

A gram of MgSO4 will pick up more water than a gram of most other drying agents but, if you put hydrated MgSO4 in a desiccator with sulphuric acid then the acid will dry out the MgSO4.

If you put sulphuric acid in a desiccator over phosphorus pentoxide you will dehydrate the acid to form sulphur trioxide.

Not may things will dessicate phosphorus pentoxide.

 

It depends what you mean by the most reactive, but P2O5 will outdo most things as a drying agent.

Unfortunately, it's expensive messy and reacts with lots of things - so it doesn't get used much.