Cool that you have seemingly been fully bitten by the Combat Sports bug and are looking into learning striking now; definitely also a good skill to have if self defense is a concern.
To answer your questions:
How long it takes before you can throw a decent punch can vary quite a bit depending on several factors such as the proficiency of your coach regarding his/her coaching/teaching skills and methods, your "natural" striking propensity (some people are more natural grapplers, some are more natural strikers), and of course how much time and effort you put into learning.
It also depends on whether you mean while under low pressure/stress and timing demands (like hitting bags/pads), or while under high pressure/stress and timing demands (like in a sparring/match or self defense context).
If you mean while hitting pads, then I'd say that a good coach should have you hitting decently hard (at least compared to the average untrained person's punching power) within a single hour long session (I can get most people there in about 5-10 minutes many times) and a really good coach should have you hitting harder than 95% of people out there within a few months. This is of course supposing that a person isn't completely athletically inept or a weakling.
If we are talking about in an actual fighting/sparring context though, then that is a different story, and I would expect to spend at least 3-5 years of serious training before you are realistically able to develop the timing, accuracy, and judgement necessary to actually start to apply real power to your punches and be able to KO most people in a real combative context.
As much as timing plays a huge role in higher levels of grappling, the lack of constant contact while striking makes the timing demands and perceptual speed demands in striking even more challenging in striking than those required for grappling.
Regarding conditioning demands, I would say the two activities are pretty equal in intensity, just different. Take a super high level striker (even a professional boxer) and force them to wrestle or grapple on the ground (especially against someone who knows how to use their weight and pressure) and they'll be toast within a round or two. Likewise, take a super high level grappler and force them to strike with an accurate, elusive striker who knows how to control distance and set point and they'll be smoked within a few rounds. The demands between the two activities just don't translate all that much to the other. You need to develop the specific conditioning for both of you want to do both well.