Just after you wash it should be enough.

Glad to hear that the wig was salvageable, Try to stick with just the oil and if you can i think that it will be better in the long run.

Yes the conditioner on the inside will seep through and coat the hair side as well and act as a mask. Just choose the colour that's the closest to the colour that your aiming for.

Hi

I wash my hair once a week. I use a heavily diluted mild shampoo and then carefully condition. You can either to this on a wig head or run the wig through water containing a little shampoo in a bowl. If you do this make sure that you  hold the bottom of the wig and pull it through the water cap first to avoid tangles. The hair is then left on a wig head to air dry. I don't use any heat tools. It sounds like the shampoo that you have used has stripped out the oils in the hair. You should get at least 6 months without problems. I am still regularly wearing a wig that I bought in September of last year. I have a new one that I wear for work because the older wig bleached in the sun. I'll probably re-colour the older one though using a semi permanent gloss.

These wigs don't get as oily (or dirty) as naturally growing hair does so you really have to be careful to ensure that you don't strip the hair of all of its natural oils when you wash it

If your hair has gone dry, try deep conditioning it and then using a little oil eg extraordinary oil or argan oil to try to bring it back. If it hasn't got to dry you should be able to repair the damage