How I can use Desktop CPU's 500 GB harddisk as external storage and what device I would need to ru

Of course, you can connect your hard disk/SSD to an Android phone. To do that you need an OTG cable. But make sure your phone supports OTG connectivity. If not, you can still connect the HDD to any other laptop or desktop using an HDD SATA cable and copy the data. Later, you can copy the duplicate files to your phone using a USB cable.
The former method is an easier one compared to the latter one.
A typical 1TB external Harddisk cost is around 5000INR.

The internal hard disk in a desktop PC is a dedicated item for that model of the PC in the sense that there will be some power supply and connecting bunches to it. If we want to use it as an external storage disk with a phone or other computer then the connecting bunches would be an issue as there should be compatible connectors available in the market. It is difficult to say whether the available ones will resolve the issue.
I would suggest to have an opinion of the computer repair technicians who can make some arrangement of connectors from some old PC and then use them for the purpose. There are no readymade standard connectors available in the market for such use of old internal drive of a desktop computer for external use.