Shimano RD TX55 Tourney TX 6/7 Speed Compatibility I currently have a 7 speed bicycle, and recently changed my rear derailleur to a Shimano RD TX55 Tourney TX for a 6/7 speed compatibility. My shifter is Shimano Rapidfire for 7-speed. 

The current problem that I have is that when I shift into the 6th, 5th, 4th, 3rd, and the 1st sprocket it becomes unstable. The RD is not properly aligned with the gears. The 7th sprocket does not have any problems. The 2nd sprocket on the other hand, I have to shift the shifter from 2 then change it to 3 only then it becomes stable in the 2nd sprocket. 

Upon observation, I suspect that the RD is more towards for a 6-speed sprocket due to their alignment on the sprockets.  

Is this true or is there some way to adjust the RD to fit the 7-speed sprocket? 

Additional information:
1. The cable is tight, not slacking. 
2. Barrel adjuster is 0, at its initial position.
Edit: First question, why did you replace the derailleur? 

Rear derailleurs don't really care about # of speeds - its the shifters which change the cable pull to move them around (so mixing shimano and sram can cause problems due to different amounts of cable pull). By RD not aligned with gears, do you mean the hanger / cage are bent? If so, go to your LBS and get them to unbend it / replace the hanger. If the rear derailleur is in good condition, you just need to adjust the cable (assuming its in good condition) to be taut when in the smallest cog (I lightly use pliers for this - make sure that the cable is actually being held in place) and then use the adjustment screws.

Have you adjusted your high low limit stops and indexing adjustment and btension?
See http://sheldonbrown.com/derailer-adjustment.html for an overview (or one of the various youtube videos on doing this)
http://www.parktool.com/blog/repair-help/rear-derailler-adjustments-derailleur

Also see the thread here: What are the most common causes for hysteresis in the rear derailler?