Both are written the same in calligraphy. Are you supposed to write ii disconnected, then?

I find it surprising that Estonian didn't opt for y and yy like in Finnish.

 

I assume the two dots of "ii" were written further apart, right above each "i".

German influence, probably.
The Finns, however, were under Swedish domination, and Swedish doesn"t have "ü" either.

 

There is not need for that, because in the reality they are very easy to detect, as AndrasBP said. Above the "Ü" the dots are more closer.

By the way, many young people using "y" instead "ü" , especially in the Internet but there are the strong distaste about this.

 

Okay, I see. If you look closely, they are indeed different.

Is it common in Estonia to write ű or ū instead of ü? (My German teacher always wrote ű on the blackboard, even though German lacks ii)

 

Yes, "ű" is quite common in the handwriting. Especially elder people uses that style more. But never seen "ū". It is Latvian letter, not Estonian as far as I know.
Estonian letters have the dots above letters - ä, ö, ü. Only exception is õ (not dash but wavy). Latvian letters are mostly with dashes above. So, for the Estonians are not natural write the dashes above the letters.