Products like 99% alcohol, C22 or Goo-Gone or De-Solve-it are all made to dissolve glue and can be used to clean the scalp & hair & base.
Some products contain oils so these need to be washed away afterwards as they will prevent an attachment from lasting.
If there is glue in the actual hairs, then soak the hairs with one of the glue melters and gently comb it through with a very fine tooth comb.

When reattaching, yes the base, hairs & scalp have to be bone dry, but heat from a hairdryer can damage the hairs and shorten the life span of your partial.

Clarifying shampoos will remove excessive product build-up from the hairs but there are certain recommended brands that are specifically for replacement hair.
Likewise with conditioners. If too much conditioner gets on to the knots, it can make them slippery and loosen the knots, causing shedding of the hairs.

There are masses of threads & posts on various products for cleansing & maintaining hairpieces.