Your question is a little confusing because you state that when you import the data, you get errors, yet all of the error messages are export errors! So I'm going to assume that the error messages are correct and you are getting these when exporting.
Your dump file has reached a 2GB file size limit. Once it hits this limit, the export utility cannot write to the file any more and you get the EXP-00002 error. If you upgrade to a newer version of Oracle, the export utilities can handle much larger dump files. Otherwise, you can use a workaround.
The workaround uses a pipe you create in the file system. The exp utility writes to the pipe, which is never more than a few kilobytes in size. You need another utility to pull data from the pipe and most use the gzip utility for this. First, make a pipe in your file system:
mknod exp.pipe p
The pipe can be seen as a file in your file system with the name "exp.pipe." Next, you'll have to start gzip to read from the pipe and export to dump to the pipe as follows:
gzip < exp.pipe > my_dump.dmp.gz & exp userid=system full=y file=exp.pipe
To import, you need to unzip the file into the pipe and have the imp utility read from the pipe as follows:
gunzip < my_dump.dmp.gz > exp.pipe & imp userid=system full=y file=exp.pipe
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