How do I merge System partition with another HFS+ partition without data loss?
There is absolutely no way that you should even think about doing any of this without a complete backup on a separate disk. Verify the backup before beginning.

1) If you have a complete backup, the easiest way to do this would be to wipe everything, make the partitions you want, and then copy the information back from your backup. If your Recovery HD is deleted, there is no way to re-create it without reinstalling the OS. (At least none that I could find when I was searching recently.)

2) Assuming you have a backup OTHER than that Backup partition, if you want to attempt to merge these, I would try it in this order: 

a. Delete the 'Backup' partition.

b. Merge 'Data' partition and former 'Backup' partition.

c. Merge System partition and other partition.

d. Re-create the 'Backup' partition and restore it from whatever backup you have.

I have done several live-system partition resizings with no problems. However, the one time that there was a problem, I had to reformat the entire drive and start over.