First comment. The 220-age is approximate. I have a friend who has gotten up to 210 at age 48. At age 50, I can almost hit 200. I can sustain 165 for quite some time. Things start to hurt over 170 (which might be getting close to my anaerobic threshold).

Question 1) Heart rate lags effort. If you jump up from sleeping and start to run - you will go anaerobic because your heart is still at rest pace. It takes about 5 minutes at a given effort (rule of thumb) for your heart to catch up. I have noticed on quite a few programmed exercise cycles they have very very short durations for effort and wide changes in exertion. Often the changes are too wide for your heart to really "catch up". I suspect that you just need to accelerate a little slower.

Question 2) You are right, your heart should be able to deliver the same amount of blood (oxygen) to your legs from day to day. So that is not the problem. What is probably the case is after a hard day you either are not motivated (which I doubt) or your legs are a bit beaten up and need recovery (repair). If my legs don't respond, I just ride "easy" and they come back in a day or so.

Question 3) Heart rate is dependent on demand for blood supply. The bigger the muscle mass exercising, the bigger the demand for blood and the higher the heart rate. This is why cross country skiing is easier to get an intense workout than cycling because you use arms and legs (more muscle mass). Think about this, could you work your heart hard enough by working on grips with your hands? Your hands are driven by the muscles in your forearms and unless you are Popeye, those are not really big. Another thing about weight lifting is most lifters lift and then relax for a bit so even if they are doing squats (large muscles) - they are not doing that many in any given unit time - nothing like the 100 rpm that a cyclist will crank out so their heart rates should not get that high. Generally, when I lift, like you, my heart rate does not elevate much at all.