[Borek]

the conductivity at the time will increase?(for second question)

See bottom of this post.

one more thing : at the equivalent point there will be any ion? i guess not right? and therefore, the conductivity is almost 0? am i on the right way?

There will be some ions: first of all, water autodissociates to H⁺ and OH^- (that's why perfectly pure water has pH 7; but its resistance is huge - something like 18.2M?.cm). Second, BaSO₄ is (albeit very weakly) soluble - saturated solution is about 10^-5M.

hey ,just now i realize that we should also base on ions to consider the conductivity , right?

Water doesn't conduct electric current. Dissolved ions do. Whenever you add more ions you increase the conductivity of the solution. But you have to think about chemistry - if you mix substances they may react, so amount of ions present may be different from what you expect. Also don't forget that different ions have different conductivities - and H⁺ and OH^- conductivity is substantially larger than conductivity of other ions.

[BaO]

thank you Borek , i feel better now .