I remember reading a thread on this forum a few years ago about what it meant to actually "deep condition". What I gathered from it was that a conditioner is a DC if it suggested being left on the hair for a period of time (3+ minutes), contained cetrimoniun chloride, or stearalkonium chloride (which allows the conditioner to penetrate the hair shaft, as opposed to just coating it), and lastly your cuticle layer has to be fairly raised by either body or external heat. I remember it saying that it takes about 15-30 for this to happen, so I always DC for at least 15 min.
These are just the guidelines that *I* follow. I know there are women on this forum who DC with everything under the sun. But for me, DCing following these rules have allowed me to no longer need to moisturize during the week, after apply my initial leave in.
I DC on wet hair because It helps with the distribution of product. But I believe the idea behind dry DCing was that your hair absorbs more product because it does not have to soak in as much water first. I've had good result dry DCing, but not significant enough to change my routine.
As far as adding oils... People do for different reasons. Oils that penetrate ( coconut, olive oil, avocado oil, etc.) can boost the effectiveness of your DC, some oils make it easier to detangle. Some think adding oil seals in more of the conditioner. My DCs usually have enough oil in them already that I don't need to add more.
You just really have to experiment with different products and techniques to find what works for you. I would start with one product, unaltered. Try it on dry hair, wet hair, heat, no heat, and for different times... and then just play from there.
HTH