Is there a way to display (enemy) champion basic information while in a match?

There is a way to see the skills of enemies altough not all i think (It's been a while since i checked it). If you die and you click on death information (seeing wich enemy killed you and such) You will see what skills did damage to you and some information, also it will show you some tips about the enemy.

Types will not be shown.

Update: So If you die you have the death recap, you can click on enemy champions and see some tips. The same as the champion screens i think. And then you can hover over some of the skills that did damage to you and get some info about them. But thats all tho.

In game, the only way is for the enemy champion to get a kill/assist on you. Then, you can review the damage and see what their abilities do.

If you have a smartphone, I'd recommend checking out some of the LoL apps. They neatly solve this problem without pulling too much attention away from the game.