Bottom Line Up Front: 2-4 weeks is a very short amount of time to get from walking time-to-time and knee pushups to a 2k* run and 80 pushups. You can exhaust yourself quickly, but your body needs time and rest to get faster and stronger. I'm going to ignore your schedule, and just talk about how I think you can get to your goals the fastest.
You'll definitely do better if you find yourself a personal trainer that understands
your goals and can adjust your routine to keep up with your progress.
I would start by giving myself the test I'm preparing for, and finding out exactly where I'm at. I'd do the run (don't just walk a distance I'm comfortable with), do strict pushups (even though it will be fewer than knee pushups) and do as many situps as I can. This can help determine how much we focus on preparing for peak performance during the test, vs building strength and closing gaps.
Do a daily warm-up routine. Even on rest days, do the warm-up routine. This should include walking, stretching and some body-weight movements to keep things moving and help reduce stiffness.
I highly recommend adding some sprints to your routine. When I say sprint, I mean as hard as you can. It is VERY easy to burn out here by doing this too frequently and your body starts breaking down rather than building up. Give your body plenty of time to rest between sprint days. I would usually say have one sprint day every 7 to 10 days or so. If you look up tabata intervals, that's a place to start. These are a mental challenge too. After the first 2, you'll probably stop trying as hard. For myself, I reverse the time sets (10s sprint, 20s rest) and find that I can push myself much harder that way. Tabatas are a proven, efficient way to increase speed and endurance quickly. BTW: sprints don't just make you a better runner, they teach your body how to work harder and send signals telling your body it needs to get stronger (possibly even releasing natural HGH).
20 knee pushups means you're ready for strict pushups, and more importantly: bench-press. It can be hard to control your loading using body weight (e.g. pushups). You can build strength faster buy using a bench. Find the weight that you can do about 10 reps, then do 3 sets of 6-8 reps. Only rest about 1 minute between sets. You are doing this right if you can't always complete the last rep of your last set, so make sure you have a spotter. Again, your body needs rest to become stronger, so take 3 days off between these workout days.
*I'm going to assume "2000KM" really means "2 kilometers" right?