In a reaction, if the concentration decreases faster, that means the reaction has a larger rate constant, and a faster reaction, and a shorter half-life. Is that a correct statement? If not, please correct me, thanks for your help :)

I think, in general, what you've said is ok. However, I don't know that this is true when COMPARING reactions; i.e., this would be ok when comparing first order with first order, second with second, etc. but I don't know about comparing first order with second order etc.