I love my body, but I want to know what exercises I should do in order to improve it and to obtain thicker and more toned thighs and legs, and a larger (more lifted) butt. My thighs are already somewhat thick, but not on a muscular level, more in a fattier way. Would my fat be able to turn into muscle? I also want to know, is there a negative effect if I only do lower body exercises? (since I don't care to improve my upper body). Also, would my diet play a role in getting a nicer lower body?
The obvious answer regarding exercises: squats. Stay away from the smith machine, please. Learn how to do squats with the barbell. They are safe when proper form is used and the safety pins are correctly set in the squat/power rack. You can just set the bar down if you fail a set. If you want to focus on posterior chain, low-bar squats would benefit you best. These would give a proper workout to hamstrings, glutes and the lower back. For the ultimate guide in form I suggest you read Starting Strength 3rd edition by Mark Rippetoe. The StrongLifts 5x5 site also has some pretty good form articles which would be a good place to start. If you want to focus on quadriceps development, high-bar or front squats could prove more beneficial. You could mix it up, of course, but progress could be slower.
Deadlift would also serve you well.
Would my fat be able to turn into muscle?
Not directly. Fat and muscle are very different beasts. Fat is fat, muscle is composed of protein (a bit simplified, but you get the idea). Indirectly, yes. If you are a beginner in weightlifting, you are at a stage where burning fat while gaining strength and muscle mass is possible, and far easier than it'd be at a later stage. The fat gets used for providing energy while the training (and a sufficient intake of protein) enhances muscularity. So while you don't "turn fat into muscle", you can lower one and raise the other.
I also want to know that is it okay if I only do lower body exercises? (since I don't care to improve my upper body).
I would strongly suggest you attempt to train your whole body. Balance is not just good for looks, but for general health. There's always gonna be a weakest link somewhere, which is what will eventually lead to problems later in life. Trying to get that weakest link stronger and not letting it lag behind too much will benefit you. Full-body workouts don't have to take ages. Beginner programs with 3 workouts per week focused on compound lifts, such as Starting Strength and StrongLifts 5x5 will give you the best return on time investment. Allowing your whole body to progress will provide a better balance in physique, which will be perceived as better looking.
Also, would my diet play a role in getting a nicer lower body?
Just like how spot reduction is generally considered impossible, so is the other way around: gaining fat to specific areas without the others. For muscles, it's a different story. Muscular adaptation will occur mostly where necessary, meaning targeted exercise can enhance a particular region. At any rate, diet will play a critical role in weight loss, weight gain, muscular hypertrophy and muscle retention. As they say, "you can't outrun your fork".
Before you are too skeptical about me suggesting strength-based programs and exercises, that you'd typically see the big burly men do in the gym, know that these will work just as well for a woman. In fact, they'll work better than anything else. Shy away from anything that uses the term "toning" or the women's magazines that can only sell copies by repeatedly coming up with new stuff that doesn't work. The basics have been established for ages and don't change, but they can't go printing the same articles every month, now can they?
You will not become she-Hulk or some scary-looking bodybuilder. With much lower levels of testosterone as men, women simply don't have the raw capacity for packing on muscle as men have. I've been training my butt off with a strength focus for 15 months now and look nowhere near what I'd like, and I'm a guy. You won't wake up one day and find "oh my, I've become too muscular". The big compound lifts, with a focus on linear progression for strength as a beginner, will provide the best progress you can get.