How can I match properties between two or more objects?
For example I have a jpeg of size 4cm by cm in my document. And I have a 2 by 2 cm rectangle. Now I want the rectangle have the size of the jpeg i.e. 4 by 8 cm in one shot. Can I match properties?
Another example is this. I have a 4.5 cm x 9 cm rectangle with orange border and grey fill.
I have another rectangle 8 by 16 cm with black border and no fill. I want this rectangle to inherit the properties of first rectangle so it has the same fill and border colour. However I don’t want to inherit the size this time, just the colours. How can I do it?
Those are two different things, with two different solutions.
You can fit the size of a frame (the rectangle) to the content (the jpeg) if you go to Object>Fitting and select Fit Frame to Content.
Your second issue is aplying aspects of one object to another. If you select the Eye Dropper tool, you can click on something you want to sample, and click on something you would like to have the same appearance as the object you sampled, and those aspects will be copied to the second object. If you double-click on the eye dropper tool, a checklist of options will come up in a window, and you can decide if you want every option, or just selected ones. Make your choices before you apply them.
You can also make Object Styles (Window>Styles>Object Styles), and any items that are assigned an object style will all update if you update the object style. This can be very useful.