You can't write using Reader. You'd need acrobat, which you'd have to pay for, in order to convert a word file into a PDF.
Abobe reader is the free version of adobe acrobat. It’s a dumb down version so that everyone can use it to view PDF’s. It has no creational ability. For that you need adobe acrobat which is mucho money! There are some freeware acrobat style programs out there, that will generate PDF’s but I’m sure word can do that as well.
Adobe's Acrobat format is really about creating a portable version of an already created document. By 'portable' I mean 'a document that can be opened on any computer running any operating system and still look the same. It's not really designed as a format for creating documents in. You can do some pretty basic editing in Acrobat, but it's not well designed for doing more than changing the odd letter here and there. And as has been pointed out above, Acrobat Reader won't do anything except open the documents. You'd need the full version of Acrobat which is a couple of hundred dollars. If you're dead set on creating pdfs (pdf = Portable Document Format = the format Acrobat saves in) then your cheapest option by far is to use OpenOffice. Cheapest because it's free! OpenOffice is an opensource Office Suite and one of its best features is that you can create pdfs from any documents you create. You'd use it just like you use Word and then when you're done with the file, you just 'save as' a pdf. ETA: Word doesn't come with built in pdf conversion. If you buy the full version of Acrobat then that comes with a plugin for Word. There are several other plugins available for word that are shareware (i.e. they cost like $20) but none has done as good a job of converting as OpenOffice in my experience. You could even write your document in Word, open the doc in OpenOffice and convert it from there.
You can't write in Adobe, but you can write it up as a Word file and then convert it. There's probably some type of free conversion program somewhere on the internet.
You CAN write in (full) Adobe Acrobat. You just cannot write with Acrobat Reader, the free program most people are more familiar with. Full Adobe Acrobat is pretty expensive. Microsoft Word is more commonly accepted for manuscript submissions. The primary advantage of Acrobat is that PDF format doesn't readjust page capacity depending on the installed fonts and printers, so you can be sure your page layouts won't change from system to system. That's really only impotant if you are typesetting rather than writing.
Not quite, by default it doesn't save fonts (or subsets of fonts) as part of the PDF. Instead it relies on you having the font or similar fonts already installed. What you can do however, is embed fonts--or subsets of fonts--in the document. But this is only really necessary if you're using a non-standard font.