Hello and thanks for asking. I see the before and after pictures that you provided. It would be better to see your own teeth but I will answer based on your questions regarding the model.
1. If the teeth are in good shape otherwise and periodontally sound (no disease, pockets, inflammation), there is a grafting procedure that can be done which essentially takes tissue from another area of the mouth ( possibly palette) and positions it so that it effectively lowers the gum line around the teeth that look 'long' to you. It is, in fact, the only way to solve the toothy appearance of the smile line. As you can see, the results vary. Doctor skill and host site reaction to the graft are variables that can cause either result that you see in both of those pictures.
I cannot tell from model pictures if you are even a candidate for that procedure or not so I will just say that good communication with your dentist is first and foremost important. He/she will let you know from a clinical examination , if that procedure is an option and will do their best to create the optimum outcome that you wish.
Good cosmetic dentistry can do wonders for patients appearance but cannot always, or even should, match model pictures. The pictures can aid in communication and let the dentist see your personal aesthetic value and that's all.
2. If your teeth are still somewhat healthy and you have decent periodontal health, no dentist would extract them and replace with implants just for cosmetic reasons. There is no implant that is as healthy, stable or as good as a natural tooth , even if the tooth needs crowns for replacing decayed crown structure or to effect appearance. In addition, implants do have their own problems. They are best used to replace one or two teeth but not a whole arch.
If you do, indeed, need extractions there are several alternatives that you should discuss with your dentist.
One- implants, provided they are few.
two- a bridge
three- a removable prosthetic device
Redoing the large , aged amalgam fillings would be a good start. It is always best to stabilize the bite (pre-molars and molars) before addressing the anterior cosmetics. If you are after a complete makeover your dentist may want to address all at once or in stages, depending on your wishes , finances and your general and dental health.
I hope this helps you make some decisions. Come back and ask more if you need further help as you move forward. Best of luck!