This is one of the springs that the drum of a washing machine is attached to. Now I want to go further into that washing machine, hopefully up to the electric motor. First I need to remove that cross-bar kind of thing which the other end of the spring is hung onto. Please suggest me some safe ways to get the spring off both the drum and the bar
Stick a crow-bar into the spring between two rotations of the coil's helix, near the top, and apply upward force to take the weight off its upper hanging point.
If needed, brace the crow bar on a temporary brace of some sort, so you have some leverage.
Then unhook or uncurl the spring, and VERY GENTLY release the force.
Best to make sure the drum is supported underneath, with some wood, so that it does not collapse if you wish to remove more than one spring.
To get the spring out begin by removing the weights (the concrete-like block in the left part of the photo). One of the studs holding that weight is just barely visible. There must be a nut just out of our view; you might need a deep socket for your socket wrench in order to reach and turn the nut. With the drum weights removed there'll be much less tension on the springs and you'll be able to lift and unhook them easier.
If your objective is to service the motor you may be going about it the wrong (hard) way. There would usually be an access panel on the rear of the washer for reaching the motor, drive belt, etc without disassembling the drum.