Yes, a SanDisk Cruzer mini 1gb drive is compatible with Windows 98, but only Windows 98 Second Edition (SE). Windows 98 SE adds additional USB support that's required.
Yes, but it may require driver software. This can be obtained at SanDisk's web site support/download section. Keep in mind the transfer speed will be below par.
All USB flash drives will require you to manually download and install the device driver before it will work under Windows 98, the driver can be found on maufactures website.