No, much of it depends on your genes. For example, people of Pakistani descent- with dark hair & skin- often grow beards faster (maybe as early as age 12) than people of Polish descent (who may be as late as age 17)- with light hair & skin. Besides, there is no rush to speed up facial hair growth since shaving just ends up being another problem. If you are concerned about short term growth, shaving will not make it grow faster, but the hair will be coarser and more even.
Honestly, no way.
You can't really speed it up but it is said shaving thickens it if you mean facial
By waiting for it to grow naturally.
Eat lots of protein.
Shave the existing hair so it comes back thicker and darker
You don't. Hair has an established growth rate. You cannot speed it up.
That's the hair growing back. You should do touch up shaving at least every other day. Shave in the direction of the hair growth. Shaving against will result in ingrown hairs and it will itch. Use scent-free lotion, too.
There are natural ways to speed up hair growth. By Applying any Ayurveda Hair oil and making the hair folicles stronger, you can get your hair live for a longer period of time. It is enough if you wash your hair at least one in a week. Try to use your nearest dermatologist [Or a Skin specialist] that you have enough proteins to grow hair. You can retain half of your hair by doing so. Hope, it helps.