Is it acceptable form to take Linux kernel source from any version, change it, claim it is mine, and then distribute it for monetary gain? In such a case open-source software is entitled to a sort of "grab, change, sell" mechanism in which anyone can just tinker with something to look different from the original source, make it work their way, and sell it as if they made it entirely themselves. Isn't that illegal?
The Linux kernel is licensed under the Free Software Foundation's GPL (General Public License) version 2. It is a copyleft license; basically, this means you are free to make copies of the original or modified kernel and sell them at any price, but the license requires you to give the same rights to the recipients: They may copy your modified version and pass it on, without paying you.
You are also required to give them the source code of your modifications upon request, not just a binary. Under the GPL, you must also retain the copyright notices by the original authors, which prevents you from claiming you wrote everything yourself.
There are permissive licenses as well. Most of them have some form of attribution requirement; but apart from that, you are free to make proprietary forks of software under permissive licenses.
I advice you first read this Wikipedia article about free software licenses. It should give you a good overview about how free licenses work. The Linux kernel is licenses under GPLv2.
Another good page about this, is the licenses page at opensource.org. There is an FAQ, which pretty much should sort your questions, as it is written in almost the same kind of nomenclature.