What are my options regarding rhinoplasty? Would my nose be a good applicant for this surgery? (photos)

First of all, your nose is very strong in its forward projection from your face. We would want to "de-project" your nose, bringing it back closer to your face. 
The woman in the short video that I posted with this answer had a strongly-projecting nose that was brought back closer in her rhinoplasty.
Then, your nose is "long," with the tip hanging low, so we would want to elevate the tip. Even if you don't want a "cutesy" nose, if the tip is not elevated, then the nose would look too long, too prominent. You can have a shorter nose and not have it be cutesy or unnatural-appearing.
The tip cartilages are strong and wide, and we'd want to narrow them. In fact, it's probably the strength of the tip cartilages that are holding the tip of your nose out away from your face and in a low position.
How much to de-project and elevate the tip? We figure that out with excellent morphs before surgery, to make sure the goals match your desires. It's not quite as accurate as making architectural plans before building a house, but it's as important.
Finally, remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose in particular needs require advanced techniques, requiring skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. 
Your nose is also a perfect example of why computer imaging is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?

Yes! You can have a Rhinoplasty to reduce the length of the nose and narrow the tip. It is important to note that Rhinoplasty is finesse surgery and all the sturtcures are like a Rubik's cube. If you change one aspect of the nose it affects another. With this in mind a careful Open Rhinoplasty to reduce nasal length, create a nice profile on the dorsum and to lift and narrow the tip is possible with a skilled Rhinoplasty surgeon.

Thank for your question.  You are a good candidate for a reduction rhinoplasty.  It is, of course, difficult to explain what to expect while typing in this space and not evaluating you in person.  The short summary :  A smaller version of your nose.  Less overall size, less width, less tip.  It will fit better with your facial dimensions.  Find an experienced surgeon, or two, and go through the consultation process.  Best of luck.