Lowerchest is part of pectoral major. The other chest muscle is pectoral minor, which sits underneath pec major to the outside of chest. You can't 100% isolate a part of the pec major, but most people believe that you can preferentially target the upper or lower fibers of the pec major by doing either incline bench (for upper chest) or decline bench (for lower chest). If you don't have an adjustable bench you'll have to be creative. If you can find some way to do chest dips that might be the best bodyweight solution.
Putting your feet on top of something (like a chair or whatever) while doing push-ups would target upper chest, so to target lower chest you could put your hands on top of something, but that's also going to shift more weight to your feet, which reduces the overall resistance level you experience.
Since you have dumbbells, if you can find some way to do a decline dumbbell bench press that'd be ideal.
A) Exactly how many sets and reps to do is hotly debated. There are countless articles in the bodybuilding community about this. For a beginner I would recommend selecting a weight such that you can do no more than 12 reps. For example, if you're using the same weight for each set you might do 12 reps on first set (and could have done more) do 12 reps again on second set with greater difficulty, and then only be able to do 10 reps on last set. I would argue that pushing yourself hard - but safely - is far more important than the specific numbers.
B) Again, don't overthink it. Doing one set of 4 reps with maximal exertion will probably give you at least 70% of the strength gains and hypertrophy of doing the perfect, holy-grail set with the number of reps, sets, and the time between sets perfected. For a whole body exercise like deadlifts or squats I'd definitely take more time, maybe even 5min depending how you're feeling, but for training chest 60 seconds should be fine and allow you to maintain pump.
C) Recovery time for chest is about the same as any other skeletal muscle. I would recommend training chest hard 2-3 times per week spaced out evenly.