What's the reaction between alkalis and some reactive metals?

I don't have that reaction in my books/

Why doesn't sulphuric acid react with calcium sulphate?

I'm not sure I understand you fully. Do you mean alkali's as in basic materials, or the Group I metals? If you mean as in a base, the only reaction I readily know of is concentrated sodium hydroxide and aluminum metal reacting to form hydrogen gas. The Group I metals will also react with molten salts of most other metals forming a Group I salt and a pure metal.

 

For your second question, just write out the formulas of calcium sulphate and sulfuric acid. You'll soon see why there is no reaction. (Here's a hint; why doesn't hydrochloric acid (HCl) react with sodium chloride (NaCl)?)

I know a little bit of acid, but I always hear of its strong corrosive ability.

I thought it can damage things which does not contain water too. With this mind, I thought calcium sulphate solid was easily decomposed by any acid.

Now I recognise acid reaction is only kinds of fast displacement reaction in the presence of water.

Yes, that's alkalis,the one neutralizes acid.