Okay, I agree with the poster before me.
If you don't like wearing wig caps then use the stretchy self adhesive fabric plaster to to 'create' a bit of scalp where your parting is. You can apply some foundation to this if you need to create scalp.
OP, I can't remember are you in the UK? If you are I get my fabric plastic from Asda for about £3. If not try attaching a bit of fabric to the wig to create scalp in the part area.
If you do go back to wig caps then you can either 'glue' the cap to your head around the perimeter to stop it from moving or if your using tape you make sure the tape covers the cap edge by a bit to keep it in place. Then apply your wig.
What colour cap are you wearing?
As for your hair sticking to the glue. I try to not tie my hair down immediately so the glue dries a bit first.
DM me if you want!