@Guy: I think both are referring to a boot splash like in other distros (ubuntu, fedora, etc.) with some sort of picture and a progress bar instead of the tc style with text messages.
@mythbu:
1. Tinycore has a compiler, you will need the compiletc.tcz extension. CFLAGS is an environment variable, you can set it globally with export CFLAGS=... or you set it right in front of the calling command, e.g. CFLAGS=... make. Then you download the sources, extract them and start with ./configure --prefix=/ or ./configure --prefix=/usr.
DESTDIR is a variable for "make install", which installs the files in a given folder instead of the root fs.
2. Howto recompile a kernel - just search in the forum, it's mentioned a dozen times ;-) However, you might not even need this step, you can use the boot code logo.nologo, if it is set at all.
3. Right, it's like remastering, you have to put splashy and directfb into your .gz file.
4. Right. Your remastering requires changing of /etc/init.d/tc-config. There you have to start splashy and move on with the progress through the whole file. When you first call "exec >/dev/null" right after the shebang it will suppress the tc messages. Now you only have to run splashy somewhere in the file.