1) Is patching really necessary to have a running kernel?
Well, patches change (usually hopefully fix) some things in the original code. To see what, read what the patch is all about. So if you're ok with the original code, have read what the patch does and come to a conclusion you don't need the patch, it's ok to leave it off -- but if it fixes something vital (like a huge crash), it's probably needed.
2) Is there any way where we can use the vanilla kernel directly (without any patches i.e) and are there any disadvantages in it?
Probably yes, just get your hands on somebody/some place that holds the original sources without patches installed. Doesn't kernel.org do this? I'm not sure..well, anyway, as I said to the 1st question, if you don't think the patch is needed for you, you're fine with it -- the disadvantages you might encounter are that if you don't apply the patch(es), some things might be broken that would be fixed with the patch. You know - patches are "fixes" of one kind. Ways to change the original code without redistributing the whole thing. Like a small repair kit.
3) I am trying to build kernel modules on fedora and am using the LKMPG 2.6 (Linux Kernel Module Programming Guide). Is it really advisable to do it of fedora? Or is there a more convenient distro?
In my opinion it does not matter which distribution you use. All Linuxes use Linux kernel, with different configurations (and/or versions) and the rest is just programs..so, no matter which distribution you chose, it's just up to what programs you install on it with which you do the job. Fedora is just ok if you're ok with the tools it provides.
EDIT: of course it most probably matters to which kernel version you write the modules for (2.4.2 is different from 2.6.10), at least a little - so pay attention to that. But besides that, it doesn't matter which distribution you choose.