In my area we pla mostly Highlander, and I always wondered about that interaction. (Also had a healthy discussion with the other players resulting in 2 opinions: Equipments always give the ability or the ability is removed)

Now the situation:
In play is a Loxodon Warhammer, 1 Runeclaw Bear equipped by the warhammer and a Grizzly Bear.
Now a Humility enters the battlefield.

Does the Runeclaw Bear still have lifelink?
The equipment adds the ability in Layer 6, Humility removes all abilities in Layer 6. Cause of timestamps the lifelink should be removed. Am I right till here?

Does it help if I equip the warhammer to the Grizzly Bear? Will he have lifelink?

What's the timestamp that matters in this situation? Is it the timestamp of the warhammer entering the battlefield(meaning the warhammer is reduced to a +3/+0 equipment) or the timestamp of the equip effect?

Does a Behemoth Sledge, that entered the battlefield after the Humility, give lifelink? (In my opinion it should give lifelink cause of the newer timestamp(s).)

Thanks in advance.

It all comes down to timestamps.

Both Humility and the Warhammer want to apply in Layer 6 (the ability adding and ability removing layer). An aura or equipment will receive a new timestamp when it becomes attached to a object or player. So if the equipment is attached to a creature, then Humility enters the battlefield, Humility will remove the abilities granted by the equipment. But, if the equipment becomes attached to a new creature after Humility enters the battlefield, the equipment will receive a new timestamp and it will give the abilities to the equipped creature.

Looking back at the original situation, if the Warhammer is currently attached to a creature and then Humility enters the battlefield, the creature will not have lifelink or trample anymore. But, after the Humility enters the battlefield, if you attached the Warhammer to a new creature, the Warhammer receives a new timestamp, so that new creature will have trample and lifelink. So if you want the equipped creature to gain the abilities granted by the equipment, you need to attach it to the creature after Humility enters the battlefield, to ensure that the equipment has a more recent timestamp.

613.6d If an Aura, Equipment, or Fortification becomes attached to an object or player, the Aura, Equipment, or Fortification receives a new timestamp at that time.