Might not be a font.

I highly doubt Picnik allows you to put your own fonts there. But try reading the FAQ below:
http://www.dafont.com/faq.php
You install the fonts, then make the video.

You'll have to pay (almost) sixty dollars to get it.
http://sudtipos.com/fonts/46
http://new.myfonts.com/fonts/sudtipos/sudestada/

Looks like one of the Didot (italic) fonts. Unfortunately I am not exactly sure which ones are them.
Just saying, Didot is used in the "Next Top Model" series.

Not a font.

You could use programmes like Fontlab, but just saying, it takes A LOT of time, effort and patience.

Yes, not a font. You could make your own if you have a drawing tablet and Livebrush.

As explained here: http://www.dafont.com/forum/read/29251/i-need-this-one-too-please
It is not a font and handwritten. Some letters ("a's", "e's", "t's" and "h's") are different. You will not be able to find it anywhere.
There are similar fonts found in, I think, YouWorkForThem.com and Sudtipos, but since they are commercial you have to pay for them.
You could try also making your own version of it.

Not a font. Not trying to sound rude, but just because you seen it on Tumblr it does not neccessarily mean that the image has been digitally altered. Someone else wrote it, with a pen or it might've been a tattoo (which I doubt a little because it looks so clear).

As explained before, it's a signature.

Probably her signature. The r's are different.
Does not look like a font, and even if it is, it could be a custom one; those can not be found anywhere, unless you try to contact its creator (which can be very hard to do). Please note that custom fonts are very costy.
There are similar fonts found here in DaFont.
Feel free to browse our database. I recommend the "Handwritten" category (http://www.dafont.com/theme.php?cat=603)
... or it could be the "Calligraphy" one?