Wizkids Rules!

Invulnerability: Basic Action
Until end of turn, when one of your attacking character dice is KO'd, return it to the Field Zone.

When character dice return to the field, do they come back on the same level as before or should they return as level 1 characters?

Further, do token characters return to the field if they are KO'd?

When character dice return to the field, do they come back on the same level as before or should they return as level 1 characters?

Invulnerability’s effect occurs after an attacker is KO’d. The Character die is moved from the Attack Zone to the Prep Area, or in some cases to the Used Pile. Both of these are play areas for unrolled dice. Therefore, this die will return to the Field Zone on its level 1 side per the following rule:

Rule 3.11.4 Dice that are swapped from an unrolled play area (e.g. Used Pile) to a rolled play area (e.g. Field Zone) will be put on their level 1 side, unless otherwise stated.

Note: Although this rule pertains to the swapping of Character dice, this principle can be applied to any Character die moving from an unrolled play area to a rolled play area: the die is put on its level 1 side unless otherwise stated.

Further, do token characters return to the field if they are KO'd?

No. For reference:

Rule 1.7.7 Tokens can only exist in the Field Zone. As soon as they leave their controller’s Field Zone they are removed from play.