Also, when I wanted to find out size of this folder with (du -sh *), it took time.In addition, I have two questions.You will probably want to use du -sh /path/directory to get the total of a specific directory. Anyway, the more files, the longer it will take to gather statistics and compute them. The same applies to the copy process. A system is usually faster to tar (archive) a directory on the same hard disk than to copy thousands of individual files to another media. The same applies to copying files via the network. The tar -v option will show you what it is doing.
1) Is this syntax the best method?(tar -zcf /home/bigfile.tgz /path/to/source/)When asking a question about how to copy files, providing information about the size of your folder/files and available file transfer options should be provided. The least information you put into your initial question, the more general or vague will be the answer. There is hardly ever a one fits all solution to any question in Unix/Linux.
2) How can I see how much time it has left to finish zip file with tar sysntax?You can't. The -z option of the tar command will compress the archive, which will slow down the archive creation process, but may result in a substantially smaller file and hence reduce the space it takes to create the archive, and time it takes to copy to another system. Time and compression ratio of your files will depend on type of file.