Tinycore is here 12/1/2008! Welcome visitors.
That depends on whether the usb stick is discovered as sdb1 or not. If you always use it with the same machine, you can use"fdisk -l" to double check.Also, it would be better to add the boot code "waitusb=10" or similar.
It is not certain, but most probably yes.
Use the UUID or LABEL of the USB stick. That way it's always found.