If you knew my answer to your first question, why would you still waste parchment asking the question when you couldn't even spare the ink to sign your name on your letter? That said, I like many charms and have different favorites for specific applications. My favorite charm to teach, however, is the Cheering Charm. Invented the 1400s by Felix Summerbee, this charm makes even a rough day much better when cast correctly. It is particularly fun in the classroom, because it only gets stronger when cast incorrectly. Third year students are often highly stressed and emotional, as teenagers normally are. It is a fine break from the gloomy faces I normally see snoozing away in my classroom to have everyone upbeat and happy, some more so than others. It is, in fact, quite funny to see some of my sulkier students be cheerful. Of course, once the spells wear off the class goes back to normal, but it is certainly a high point in the curriculum each year.
As far a spells to make one "go invisible", no charm truly does this for a particularly long time. The Invisibility Charm can create an effective field of invisibility around the object it is cast upon, but it wears of fairly quickly as far as spells go. Of course, the Disillusionment Charm can produce a similar "chameleon" effect, but it does not truly render you truly invisible. In terms of making people like you, I feel very strongly that charms should not be used to change someone's preferences without the permission of that person beforehand. That said, such mood changes are likely more the job of potions than charms. Perhaps you could try something more specific. For example, you could give someone flowers (preferably not the honking variety) to try to woo them. If people dislike you because you are surly, maybe a cheering charm could do you some good. As for wishes, it would depend what you were wishing for which charm might do the trick!