I have always encouraged the 'showing of answer cells' as late as possible. Just like you mentioned, it is unique at LMI and I dont suggest to change it.

1 possible solution is to enable an 'Answer Page' for offline solvers after some time. This page will mention the row/column to be entered in one line. The drawback is that the pdf will not have marked arrows, so it is error-prone. But it is still an idea.

That is definitely error prone for paper players. Also, it significantly increases the chance of 'organizers' doing mistakes.

One of my earliest thoughts (after reading this post - http://motris.livejournal.com/120480.html) :
Everything remains as is.
Add two text boxes below each grid.
Paper players can enter the solution in the text boxes.
Does that help? It still does not solve the problem 2 and 4 you mentioned.

Again - just one possible idea. Other ideas most welcome.

Yes It helps.............

We are adding a text box per grid in the next Sudoku test.

Here is a screenshot

This is a wonderful addition to help people solving on papers... However, if we find that a person has erronously filled the online grid and the textbox below..then by default the answer in the online grid will be taken as final answer!

Thanx Deb....this is really wonderful...........

Thumbs up from my side.

Superb!
Will get much easier for people solving on paper... :)