Can I transfer music from my computer to ipad?

Yes, you can transfer music from your computer to your ipad but you would need to install Itunes to do that and Itunes is a free software you can download. Yes, there is a free Kindle app at the Apple Store. And yes, you can put movies to your iPad. If those are movies you didn't purchase from the Apple Store, and if their video format is like AVI or MKV, you would need a third party software to convert them into files that iPads can read. Regarding a pdf reader, I haven't tried that. Although you can install the iBooks App that reads PDFs.

You can sync music and other content to an iPad via your computer's iTunes (a free download from here) - you don't have to purchase anything in order to use the program. You can buy music from Apple, from other sites and/or copy your own CDs via iTunes, and then sync them to the iPad via iTunes.

Syncing music : http://support.apple.com/kb/HT1351

I don't know what country that you are in, but there is a Kindle app available for the iPad in a number of countries (the app is free) which can be linked to your Amazon account so you can download your kindle ebooks into it. There are also Nook and Kobo ereader apps.

There are also a number of PDF reader apps for the iPad, some of them free like Apple's iBooks and Adobe Reader, and some which are paid-for which are more powerful e.g. GoodReader.

Films can be purchased from Apple, or there are other sites such as Netflix with their own apps. The iPad natively supports a number of video formats (they are listed on this page).

There is a manual for the iPad here which has some info on it's built-in apps (plus iBooks which is a free download) : http://support.apple.com/manuals/ipad/

No you aren't tied to purchasing from them. To sync content from your computer you will need to install iTunes on it, but you can buy music from other sites and add them to iTunes and/or copy your own CDs, and for ebooks Kindle, Nook and Kobo are all available in the US.