WordPress on localhost

»2 – Can i install the current wordpress that i’m using in Computer A (at Work) in to Computer B (at Home) so that i can continue programming in Computer B what left to do in Computer A? And how can i do that?!

Assuming I have correctly understood the work installation as being localhost in WAMP, you can duplicate that at home by doing the necessary installations (WAMP and WordPress) at home and then “moving (copying) WordPress” from work to home by importing the work database and adding the content of the /wp-content/ folder:
https://www.google.com/search?q=moving+wordpress

To do that, carrying things home on a stick might be the simplest way rather than trying to use an FTP/SFTP connection to either machine, and then you might or might not have to do some database updating if the drive paths on the two are not identical…

note: Edit ‘pref’ (three places below) to your own table_prefix and change ‘http://www.olddomain.com’ and ‘http://www.newdomain.com’ as required (three places each and with no trailing slashes)

UPDATE pref_options SET option_value = replace(option_value, 'http://www.olddomain.com', 'http://www.newdomain.com') WHERE option_name = 'home' OR option_name = 'siteurl';
UPDATE pref_posts SET guid = replace(guid, 'http://www.olddomain.com', 'http://www.newdomain.com');
UPDATE pref_posts SET post_content = replace(post_content, 'http://www.olddomain.com', 'http://www.newdomain.com');

Disclaimer: The above is all theoretical since I have never actually done that.

As to syncing the two installations on an on-going basis, no problems should arise from using a stick or whatever to transfer (copy) /wp-content/themes/ and /wp-content/plugins/ from one machine to the other, but /wp-content/uploads/ and the database would be a different matter since uploads must be registered in the database and the simplicity or complexity of syncing the two databases would be dependent upon the above. In my own case, I often just copy-and-paste from the page/post editor at one site to another while having the two side-by-side in a browser, and you might be able to do something similar (and then also deal with the matter of any new upload/s) if actual content is what you are trying to sync.