For your first foray into growing, a full spectrum bulb will work good for you, although make sure you have enough light. You didn't specify the size of your grow area or size of the bulb, but things seem to be doing OK.
Why did you cut off half of the leaves? Rooted cutting are fine as long as they have decent roots on them, although I usually prefer my cuttings to be a little larger. After the cuttings are rooted and established, treat them like seedlings until they grow another set of leaves or so. After that, they are the same as any other plants, so feed and water like normal. The re-vegged plant might look pretty strange, but it is all good.