I had my most recent tattoo done almost a year ago, and for the early care I was told to wash with an antibacterial soap we have here called Dettol. The artist said not to use the foaming handwash kind, but instead use the plain unscented bar soap from that brand. The lotion I used was some kind of diaper rash cream, I forget exactly the name of it... it was a clear gel/ointment that I had to reapply every few hours, more often if I was wearing clothing that covered the tattoo and might rub the lotion off.
Two weeks sounds about right for healing time, though some spots may take longer to heal than others if the needle went slightly deeper into the skin at some point. I had a couple spots on mine where several outline lines intersected that took a few days longer than the rest to fully heal. I had 1 spot that randomly scabbed over a few weeks later, but even after it healed it didn't damage the design much. If I didn't know that slightly scarred spot was there I probably wouldn't even notice it. The point is to avoid scabbing as much as possible, it can and will cause fading and damage to the design.