Why need to check the partition before conversion? And How?

As the error file could not be converted to FAT32, so try to check mistakes and fix them by chkdsk.exe. The operating process as follows:
A. Click "start" -> "run", then, input "cmd" and enter into the command line console.
B. Enter "chkdsk.exe X": and start the X partition checking. (If want to check C partition, input chkdsk.exe C :)
C. If found mistakes in X: partition, please input "chkdsk X:/f" to fix the mistakes.

There are some compressed and encrypted files featured with NTFS, can the NTFS to FAT32 Converter deal with those?

Yes. As compressed and encrypted files could not be supported by FAT32, therefore, for user's data security, NTFS to FAT32 Converter is designed to decrypt and decompress the files automatically. You just need to operate the software according to its prompt. The data security must be ensured.

Is it possible to convert a partition larger than 32GB to FAT32?

Yes. The windows built-in disk management and other utility don't allow that, it is not a problem for NTFS to FAT32 Converter, the maximum supportable size of partition up to 2TB.

How much time it should be taken to finish the conversion?

The time should be taken bases on the number and total size of the file on NTFS partition. In general, a partition with 40GB data will cost 10 to 20 minutes, but, conversion for a partition without any data just needs seconds.

Could NTFS to FAT 32 Converter help me add the single data which is larger than 4GB into FAT32 partition?

No, the converter could only help you convert partition from NTFS to FAT 32. The FAT 32 file system could not support single data which is larger than 4GB, this peculiarity is designed by Microsoft.