Grafkapador is completely right about the level of pseudoscience floating around about this exact topic. As a specific example I think I remember an episode of "Stan Lee's Superhumans" with someone who claimed to have uncanny control over their heart rate.

Nonetheless, there is perfectly good evidence that the answer to your second question is a definitive yes, and my personal experience certainly confirms it. As noted in the beautiful explanation of heart anatomy and control systems, you have two (three if you separate norepinephrine from epinephrine) chemical modulators of heart rate.

As it so happens - and as noted above - both of these chemical modulators can be consciously controlled. I find it odd that Graf said "you can not consciously modulate your heart beat beyond psyching yourself up/down" rather than "you can consciously modulate your heart beat by psyching yourself up/down". While it's true that there doesn't seem to be any "direct" control over heart rate such as modulating it just by thinking about it beating faster or slower, psyching up/down is definitely a "conscious" process which can be done either in the presence or absence of physical stimulus.

For example, you can be doing vigorous cardio exercise, but if you are an experienced practitioner of meditation you can very rapidly bring your heart rate back to 70 or 80 bpm (probably not all the way to 60 unless you're also an athlete). At the same time, you can be sitting in a chair or lying down in bed and can get your heart rate up to 140 bpm or higher just by pumping adrenaline.

While most people think that an adrenaline response requires a strong stressful stimulus, that's not ubiquitously true. Simply remembering a stressful situation, thinking about danger, or falling/flying can trigger an adrenaline rush and push your heart rate above 140bpm.

WARNING: personal anecdote time

While everything above is pretty scientifically and psychologically well supported, I'd like to add something which is not particularly well studied and comes from personal experience.

I spent a lot of time when I was growing up meditating, I practiced many different forms of meditation including trances, visualization, deep relaxation, and "psych-up" meditation. While initially the "psych-up" process involved having to think about something exciting/stressful, I eventually learned that just by breathing more rapidly and recalling previous psych-ups I could release large amounts of adrenaline without thinking of something stressful. It has been over a decade since then and I'm now able to release enough adrenaline to dilate my pupils significantly, give myself goose-bumps, and raise my heart-rate over 140bpm and my blood pressure to at least 160/90 without even changing my breathing, only by thinking about the adrenaline release.

My mastery of acetylcholine release is lagging behind significantly. While I can get my heart rate down to 80 bpm from 140 in a matter of seconds after exercise, it requires deep breathing, calm thoughts, and stopping the exercise.

The Dalai Lama attended a meeting of neuroscientists in America some time ago and issued them a challenge to understand the scientific basis of how meditation improves them mind, and how buddhist monks achieve some of the amazing feats they do. While some of what I've said is not yet confirmed by science, it is the subject of active scientific research - and not just pseudoscience. I believe that very soon we will come to a very thorough understanding of this topic, and that a definitive scientific answer to your question will be available, and that the answer will be a resounding yes.