Do skills carry over with levels?

For example, if I acquire the level-2 skill on the light/fast attack 'tree' and activate it (by placing it in a 'slot'), does the level-1 skill too get activated by default or do I have to equip it in another 'slot' for it to be active?

So basically, does activating a skill in a skill tree activate all other skills above it by default, or do they have to be placed in separate slots?

You have to equip skills in slots to have them active, lower level or not.

Each icon is a separate skill that needs to be put in slot to be active. Everything outside the skill slot is not active.