How can I change the default pin positions of Eagle library components ?
By which I can root component-to-component connections in a schematic as I like.
For example in NE555 symbol I want to change pins 6 & 7 from the left side to bottom side.
You must change the symbol in the library to move pins where you want them.
Best would be to copy the symbol and create a new one with rearranged pins. Assign the package and connect pins and pads when creating a new device, e.g. NE555-1.
You should refer to Eagle tutorials to understand how it's done. You can only reduce the size of components in the library itself using the editor.
It makes no sense to me to shrink a DIL package.
You have to keep three terms in mind concerning any schematic & layout software. A component is a DEVICE consisting of a symbol (that appears in the schematic) and a package (which appears on the PCB). Both symbol and package must be combined to "compose" a device by assigning pins (of the symbol) and pads (of the package) to CONNECT using the assigned package.
Here is a selection of NE555 timer ICs to use dependent on their purpose. The attached library contains all five types, where NE555-B means basic IC, NE555-A means astable (for enough space between pins 7 and 6 for a resistor), NE555-M is meant for a monostable, and finally NE555-A-N and NE555-M-N for no power connections which you can INVOKE on demand.
Many schematics containing power connections directly at the symbols become confusing easily, especially if signal nets run adjacent to the supply nets.
Creating a separate power block keeps the schematic clear and neat.