When two card texts confict, which takes priority?
How is this situation changed if True Conviction were in play?

It doesn't.

Is the situation changed if True Conviction were played after Humility?

Yes. Each creature of the controller of True Conviction will be a 1/1 creature with Lifelink and Double Strike.

Is the solution to this question that the card with the newest time stamp is in effect?

Yes. Section 613. Interaction of Continuous Effects of the Magic Comprehensive rules describes the order continuous effects are applied.

613. Interaction of Continuous Effects
613.1. The values of an object's characteristics are determined by starting with the actual object. For a card, that means the values of the characteristics printed on that card. For a token or a copy of a spell or card, that means the values of the characteristics defined by the effect that created it. Then all applicable continuous effects are applied in a series of layers in the following order:
613.1a Layer 1: Copy effects are applied. See rule 706, &quot;Copying Objects.&quot;
613.1b Layer 2: Control-changing effects are applied.
613.1c Layer 3: Text-changing effects are applied. See rule 612, &quot;Text-Changing Effects.&quot;
613.1d Layer 4: Type-changing effects are applied. These include effects that change an object's card type, subtype, and/or supertype.
613.1e Layer 5: Color-changing effects are applied.
613.1f Layer 6: Ability-adding and ability-removing effects are applied.
613.1g Layer 7: Power- and/or toughness-changing effects are applied.

Humility is an ability-removing and power/toughness changing effect. True Conviction is an ability adding effect. Since both effects use the same layer 6 and aren't dependent upon one another, the order the effects are applied is done in timestamp order.
Also note

613.5. If an effect should be applied in different layers and/or sublayers, the parts of the effect each apply in their appropriate ones. If an effect starts to apply in one layer and/or sublayer, it will continue to be applied to the same set of objects in each other applicable layer and/or sublayer, even if the ability generating the effect is removed during this process.

So the power changing effect of Humility will always be applied last, no matter what.