First off, I'll let you know I have 2 full makeup races with rather involved paint applications. I also do a good deal of the detailed makeup for NPCs in SoMN monster camp as well.
Barrier Spray: This is something you can pick up from a costume store or online that will keep makeup from seeping into your pores. This keeps your skin happier as well as making the cleanup much easier. Other benefits of it are that it somewhat inhibits you from sweating in those areas and can be used to set a powder makeup. It creates a translucent barrier between your skin and the makeup. The websites
say that it also helps lessen makeup sensitivity in some folks, but I'm way too jaded about my somewhat severe makeup allergies to try using a non-hypoallergenic with it. I make all of my NPCs put this on before full makeup jobs. It stings a little bit like hairspray for a second after it's been put on your skin, and I have heard a few guys comment about how it hurts when put on freshly shaved skin (it's alcohol based) but it really does make a difference.
Brushes: Yes, you can apply cake makeup with brushes. I do it all the time. For brushes, an acrylic brush will stay unfrizzed longer, but some folks are more partial to natural fiber brushes. I use an acrylic brush set I picked up at Michaels as it gives me lots of maneuverability with the different brush sizes and shapes. This would work well for the green. Remember to always wash out your brushes!
Eyeliner: The reason you might want to go with a liquid eyeliner for the outline is that liquid eyeliner is generally waterproof and is made to not smudge. I use it occasionally in monster camp for runes and other small, defined shapes and patterns with great success. The way it is packaged makes for a very clean makeup process, as you have your brush and makeup conveniently secured in the same small tube. Even for a design the size of what you're planning shouldn't use too much of it.
Makeup: There are two types I would recommend for someone if they haven't used much makeup before. The first is Mehron Paradise (it's hypoallergenic). The reason I recommend this one is that it is easy to apply, cleans up well (unless you're going with red... then you'll be a lobster for a few days), and is relatively harmless for your skin (really anything you put on your skin is doing some harm though). This one makes for a pretty clean setup, especially if you're using brushes. Being a cake, this does need water to get it workable. I would recommend bringing a bottle of water for setup just in case you either don't have running water on site or someone else is using the bathroom. The second I'd recommend is actually Halloween store cream makeup. The brand I use is Backstage. Reasons: It's cheap, dries pretty quickly if you don't put huge amounts on, will stay on pretty much all weekend, and it's easily found. This one might be a little more messy to apply though, as it's sold in a tube.
Smearing: To stop the smearing, you have several options and thoughts to consider: Do you sleep on your side? If so, which side? Do you toss in your sleep? Do you want to do your makeup once and be done, or do you want to take the time in the morning to retouch/redo it? Do you habitually touch your face? Stop that.
The easiest, but definitely not cheapest way to not deal with smeared makeup is using airbrushed makeups. With the sharp edge you want, I'm not sure that is your best option. Setting Powder is another option. Translucent would be your best option here, and make sure to apply it with one of those fluffy makeup brushes. Works well from what I've heard, but I normally use option 3... Touch up when needed! I make a habit of not touching my face, and I check in on how my makeup is doing whenever I'm in my cabin or the bathroom. With the size and placement of your design, the only foreseeable threats to your makeup are smearing from sleeping, getting hit in the cheek, excessive sweating (some people just sweat a lot), and from you touching your face.
Cleanup: Another thing you want to think about is makeup cleanup. I carry baby wipes in my personal kit to start the process and for sites without running water (my main character is full makeup, main site is extremely basic... why do I punish myself like that?). I also keep an acne scrub (I like the apricot scrubs) for getting into the pores, and a bar of dove soap for final cleanups. Always bring your towel!
By the way, I don't think that is really a 'simple concept sketch'. It looks great!