How to check if an available update will take up more storage or less than the one currently installed version? How can I check if an available update of a given app that I already have installed will take up more or less storage space than the one currently installed from the information in the play.google.com page? Is there a URL I can use to check the size of my current version and the one of the available update? Can I mount the device and list the size of the installed apps and compare it to the advertised size in play.google.com?

For example, I updated Gmail in the last few months, and originally took up 2.07MB Application size, and the last two updates went from 3.08MB Application size to 3.26MB version 2.3.6 (20110305). How can I know this in advance?
Current App's Usage:


If you mean storage, there's a handy program on market called Disk Usage. It will display the current size of all installed applications, as well as how much space each's data takes up. 
I have a feeling you may mean RAM usage, which is a different animal indeed. To get the amount of RAM a program is currently using, see the Apps section of the Settings.  The Running tab shows the relevant details.


New Update's or Non-Installed App Usage:


Most of these details cannot really be determined before installing an app or an update, unless the developer is kind enough to include these details in the applications's description or the What's New section.  The closest you can get is the actual size of the application, which does show up in the application description.  I guess you could use a combination of what you can learn from Disk Usage on the current version's size and correlate that to what shows up in Google Play for the current version.


Details like RAM usage are difficult to determine as they depend on a lot of factors:


Which resources are loaded on your particular device configuration (e.g. high or low res images and icons).
How you use the app (e.g. if you have a browser and load 100 tabs, the program will use more RAM).
The quality of the app.  The program may inadvertently waste memory due to a bug only you experience.  It would be difficult to predict things like this.


As for app storage, this really depends on whether the app developer chooses to change the way it stores data.

Hopefully this answers your question.