Hi fitito,
It is yes that JA Wall can work on your localhost.
If your computer can connect to internet, it will run well.
If not, then those extensions which required for internet will not run well.
I would recommend you use WAMP.
http://www.wampserver.com/en/
Please download this file: Wampserver (32 bits & PHP 5.3) 2.2E (Apache 2.2.22 – Mysql 5.5.24 – PHP 5.3.13 XDebug 2.1.2 XDC 1.5 PhpMyadmin 3.4.10.1 SQLBuddy 1.3.3 webGrind 1.0)
It will run well on window 32bit or 64bit.
1. Stop Skype
2. Install WAMP (I would recommend you use other harddrive (not C:))
3. Then just copy and extract the JA Wall quickstart package to :wampwww folder.
4. Create a database by phpmyadmin (http://localhost/phpmyadmin)
5. Navigate your browser to JA Wall package folder and start installation.
Hope it helps.
Regards