Looking for feedback on my workout

rapat

I've been following this the past two weeks. Would be interested in some feedback or suggestions

Limitations: There's no barbell at either my apartment (I live in a highrise) or work gym and I stopped doing back squats due to past issues/injuries.

I do upper body exercises while at work.
I basically leave my desk for 5-10 minutes, do one exercise to exhaustion, go back to my desk, do the next exercise an hour or two later. This should be fine as long as I do a warmup set before each exercise?

Monday, Wednesday, Friday:
DB Chest Press
DB Shoulder Press
DB Bent over Row
DB Bicep Curl
With the above, I've been using a reverse pyramid -- a warmup set or two, then a set with my max weight to failure, then dropping the weight by 5-10lb and doing the next set to failure, and repeat the process till I've gotten 5-6 sets. If I can do 10reps at my max weight, I increase the weight next time.

Sunday, Tuesday, Thursday
Pullups -- cycle between neutral, underhand, overhand to failure each set until I can't do 1. Then do negative pullups ~5 times
Dips -- keep doing sets to failure until I have trouble getting 1-2 out


Lower body & Cardio --

In Mornings: 3x a week, just on random days:
Quick Treadmill Running --
a half mile run, a quarter mile run, and a 1/10 mile run with recovery to 120hr in between.
Trying to increase my pace each time by .1 - .2mph
Currently at 9, 10.2, 11.3 mph for each
Machines -- Leg Press, Curl, Extension.

25-40 minute bike or rollerblading 2x a week on random evenings

Ice hockey game once a week


Questions:
I'd like to get some core work in as well.
Should I schedule that on my pullup day? Any suggestions for exercises?
If I did pushups, should I do them on the chest press day, or on the recovery day?
I also do plyometrics irregularly -- box jumps, etc. If I do those more regularly, should they be done on the same day I do leg machine work, or on the days I don't?

Any other exercises I can / should add in?