For small, mildly, atypical moles, using a punch biopsy to remove the entire nevus is reasonable. The specimen will be reviewed by a pathologist to confirm that the margins are clear. Larger, atypical moles often require excisions because the punch biopsy instrument may not be large enough to completely remove the lesion. Severely atypical moles are often treated like melanoma in situ (the earliest form of non-invasive melanoma), and excised with 5 mm margins. Your dermatologist will usually get a report from the pathologist identifying how atypical/concerning the mole is which guides further treatment. In your case, it sounds like they are proceeding appropriately.
A small gauge needle is used to inject Juvederm, but any time a needle penetrates the skin there is a little red mark, and usually a little bleeding. These spots will fade over a day or two. If you bruise from the injections, which is not uncommon, you will notice that the bruises take up to 2 weeks or so to completely fade. Usually after a few days these bruises are easy to camouflage with makeup. I usually recommend that my patients get their Juvederm the Thursday or Friday before a weekend where they don't have any important events.
Developing a droopy eyelid after botox is largely due to incorrect placement of the injections by your doctor. There are certain anatomical landmarks that should guide your doctor when injecting botox, and you're unlikely to get a droopy lid if botox is injected appropriately. It is not unusual for patients to receive 30 or even up to 50 units to treat the entire forehead, including the glabellar area. Even when a doctor adheres to all the "rules" of injecting botox, complications like a droopy lid can occur, but this is rare. Botox is safe and very effective. As mentioned in other posts, there are eye drops that can help with your temporary droopy lid post-botox.
Sometimes a little crusting does occur after laser treatment to treat nasal telangiectasias (the dilated blood vessels), especially since these are more stubborn and require a little more vigorous treatment. Most wounds, including yours, heal the best when they are kept greasy and covered. The goal is to avoid scab formation. Since you probably can't (and don't want to) cover your nose, I recommed using polysporin, or even a bland emollient like aquaphor several times a day. There is no need to remove the crusts - they will soften and fall off on there own if you keep the area lubricated. If the oozing persists, contact your doctor to make sure you are healing properly and have not developed an infection.
The effects of Botox diminish over time, with most patients needing a repeat treatment after 3-6 months. There are several factors that will determine how long your botox will last: the amount injected, the strength of the muscles injected, and the location of the injections. Often, after several treatments, you will not need botox as frequently. This occurs because your muscles get out of the "habit" of contracting.