First one, yes. Set up this in a tech

     <GameModifier>
            <ModType>Player</ModType>
            <Attribute>AbilityBonus</Attribute>
            <StrVal>A_Traits</StrVal>
            <Value>1</Value>
            <Icon>UnitLevel.png</Icon>
            <Provides>+1 Trait on Designed Units</Provides>
        </GameModifier>

Second question: No, not without adding a 5th slot to all champions in the game (and I never got that to work either).

They have no maximum cap of traits so not really.