A cheap beginner airbrush works wonders
Here's a 20$ airbrush kit on Amazon
This is one of the props I just finished with this exact air brush kit
Also, if you want that exact color of paint for said airbrush without breaking the bank on spraypaint cans, Home Depot sells sample colors, 7~oz, for like 3$. You can get any color that multicolored wall, and I think they can scan custom colors too. Mix 50/50 with water and it works wonderfully.
Nice sharp edge can be done with what you have pretty easily. Say you're making a yin-yang sign. You have a black circle. Put down your tape where you want your white line to be. Airbrush some black on there lightly, just enough that it kinda wets the tape. Let dry, then paint your white on there. With a knife/razor, carefully peel the tape off. Painting the same color before the new color allows it to fill into the cracks and gaps left by the tape
As for filling the grooves, the technique you want is probably called dry brushing. With a dry paintbrush, take some paint the color you want, fill the gaps, then wipe at it with a wet paper towel. Punished Props has a lot of cool guides