I don't mean to be discouraging but your routine could use a lot of work. It barely even relates to the goals you listed and is random at best.
First off, circuits are almost useless for anything but endurance training. You can't get strong with a circuit because your body doesn't have time to rest. You'll make gains initially but your progress will stall very quickly. Some very general ranges are 30-90 seconds rest for endurance (muscular, not cardiovascular), 90-180 seconds rest for mass, and 3 minutes+ rest for strength. For now I highly advise you focus on strength because strength translates to endurance much more than endurance does to strength.
Start off with a wrist warmup/mobility program. Preferably warm up your whole body. Light aerobic exercise and mobility for all your joints should do the trick.
After that comes skill work. This can include planks (because they're mostly for posture/body allignment) if you don't do them to the point of exhaustion and do them with the right form. If holding it for 30 seconds isn't extremely hard I guarantee you're doing it wrong. If you want to do them last that's also fine and then you can use them as a finisher and go to exhaustion. Your choice. Also, you can throw handstands or
light parkour training in here but legitimate parkour training should be done either different days than your workouts or several hours after.
Next comes strength. You don't even have l sits in your current routine so if you want a 15 second l sit you need to change that. Do l sits first and do them on the floor. Watch this video
http://www.youtube.com/watch?v=IUZJoSP66HI and a 15 second l sit shouldn't take you too long.
After l sits do strength movements. Since you want to achieve a muscle up do pullups first and drop the clapping pushups for dips. Pull up as high as you can, dip low but be careful not to hurt your shoulder. This will also help your climb ups but you need to practice those separately as well since there's skill involved.
If you want to bench your bodyweight you need to bench. 3-5 sets of 3-8 reps (I'll explain this more if you don't know what I mean). Add in some kind of rowing as well.
http://www.youtube.com/watch?v=TZDKBnuOLFg This is a bodyweight row. Harder if you elevate your feet. Try to match reps with benching.
If you noticed this is pull and 2 push exercises. This is
extremely important. If you don't balance out pushing and pulling you
will develop shoulder injuries that are extremely debilitating. Don't do more than 2 push and 2 pull at first. It's too much volume for most people and can kill your gains.
Do something for your legs along the same lines. Squat and deadlift preferably but also pistols, glute ham raises, etc. Just pick 1 or 2.
So drop the circuit, rest about 3 minutes between sets, and shoot for exercises you can only do 3-8 of. When 3x8 becomes easy pick a harder progression except for pullups since you want 20 just keep working those.
Also, l sits and planks are enough for your core. If you want more exercises do hanging leg lifts but drop the crunches. They're very hard to do right and there's serious potential for a back injury when they do just about nothing for you except increase the amount of situps you can do. They're only necessary if you want to join the millitary where you're specifically tested on sit ups.
If you have any questions about anything I said ask away and I'll happily go into detail/explain what may sound like blasphemy.
