1+2) download the vanilla kernel sources from
www.kernel.org and apply the desired patch, e.g.
cd kerneldir && patch -p1 < ../tinycore.patch
the (patched) source for the tinycore kernel can be found on the ibiblio mirror, there's also the patch available. due to special adjustments, the patch will not apply on any other than the 2.6.29 series, so no "real" upgrade possible atm
3+4) patching/upgrading a binary format extension like .tcz is not really possible, if you want to upgrade it or change it, then create it yourself. after that you can mail the originator of the extension in the repo and ask him, if it's ok replacing his version with yours.
if you want to build your own extensions I would suggest you read the forum topics, there are several build scripts, which easily allow to create extensions. dependencies can be found during the building process (looking at the output of ./configure or ./configure --help), it just requires a little experience, which cannot be written down as a tutorial.
binary files from other distros will certainly cause problems (different arch, compiler, flages, etc.), so it's not advisable to create an extension out of them. frankly if I was the repo maintainer I would delete those extensions without asking ;-)