I’ll try and answer these:
# I’m not familiar with the rock climbing plan in particular, but if you’re new to structured training in general, then a lot of Zone 2 work shouldn’t be a problem. If you’ve done years of structured training, and if you’ve seen the top of Zone 2 come within 10% of the bottom of Zone 3, then you may want to add in some easier volume.
Going by feel, how hard is Zone 2 for you? Would you describe it as “no big deal, I can do this all day”? Or “oh man, I don’t think I can sustain this over the long-term”? Or somewhere in between? Both are possible in Zone 2 depending on the training history of the athlete.
# If you feel like DOMS (Delayed Onset Muscle Soreness) is interfering with your aerobic work, then you may want to back off. Again, this is a judgment call about the overall impact of the strength training.
# I would recommend changing up your training modes as required physically and mentally. So long as the modes are weight-bearing–i.e. cycling will not be a great substitute–then you should get a similar benefit from running, hiking, and box steps and can increase duration without monitoring durations per mode.
Of note, I have similar issues with flat running. I find 45-60′ the limit for my hips and head. Trail running, however, is way better, so you may want to give that a shot. I suspect that I have fewer issues with trail running because the variable running surface and changing grades keep the motion less repetitive.
I hope that helps.