1. wifi: can you download the wifi modules for tinycore from another machine? if yes, then go to this address:
ftp://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/and download the appropriate modules for your version of TC; put them on a usb, make a tce directory at the top of your hd or of your usb (mkdir tce) and save the modules into the tce dir so that they will be loaded at boot;
2. mount your usb stick with the mount tool in the cpanel, or in an aterm, type: sudo mount /dev/sdXY /mnt/sdXY (where X is the letter of your usb, and Y the number; do sudo fdisk -l to see which letter and number has your usb stick); to unmount your usb, in an aterm: sudo umount /dev/sdXY
3. save your settings, Java: search in the forum and look at the FAQ, there were lot of discussions about this; for Java, don`t forget to load OSS and to run the browser once before installing Java.