Hi CR
No scrubbing the lace base - it is too delicate for that. The lace has to be cleaned gently. There are various methods. I use tape and glue, and I soak mine in alcohol and then scrape off any residue with my fingernail or the edge of a credit card. Some people cover spent glue with cotton wool and then rub the glue/lint combo off as boogers. That works quite well too if you only use glue.
Once the lace is cleaned, then you can apply shampoo to the base and the hair, and clean them both by squidging the suds through them. Again, be gentle. When the knots are wet they are lubricated and more vulnerable to being tugged out. Treat the piece like you would treat your favourite cashmere sweater.
When you rinse the shampoo out, make sure the water is always running from the underside of the base through to the upper side, so that hairs are not being washed through to the underside.
You say you are not planning to use conditioner, but I think you really have to use a good quality rich conditioner any time you shampoo the piece. However, conditioner has to be kept off the base and the knots. I scrunch the lace base up in my fist and hold the skein of hair tight just above the base. Then I put the conditioner on and comb it through the hair, using it as a detangler as well as a conditioner. So, in answer to your question, yes you can brush/comb the hair when it is wet, so long as there is no tension on the knots. Once the conditioner has done its stuff, I hold the skein of hair under the running tap and let the water wash the conditioner out, and again you can be brushing the hair during that process to keep tangles out.
Finally, I lay the hairpiece on a towel still in a skein of hair, then roll the towel up into a sausage. Then I press the sausage to squeeze out any water into the towel. Then take it out of the towel, straighten out the base, put it on a polystyrene wighead to finish drying naturally, and comb the hair into rough shape.
I'm sure there are other methods, but this works well for me.
Noah