When activating tornado wall while umi is on the field, do i get damaged by paying lifepoints? e.g.( toon world)

Yes you do. Tornado wall only stops battle damage inflicted to yourself by your opponents monsters. Paying Life points and card effect damages like Ring of Destruction still affect you.

Read the card AND rules closely...

Payments and "decreases" of Lifepoints are NOT the same as "damage," so Tornado Wall DOES NOT prevent them from occuring.

Also, Tornado Wall only protects the CONTROLLER of the card from BATTLE damage. So any damage from effects still place and monster's will still be able to die in battle (but you won't take LP damage if the ATK is higher of if they have trample or something).

From what I know and have done, Umi and Tornado wall combo is pretty good but has disadvantages.

if you read the card tex carefully, you wil notice it says battle damage, not LP damage from cards like Solemn Judgment and Ookazi and others.

So bottom line is....

Protects Battle Damage, but you are prone to other card effect damages, (i.e.-Catapult Turtle)

Sidenote....Solemn Judgment is NOT "LP damage" it is payment...as is Delinquent Duo and "Decreases" like The Immortal of Thunder and "Losses" as well.

Think of Tornado wall as an all cover Kuriboh. What does Kuriboh Protect against? Tornado does the same job Kuriboh does.