first of all let me point out that you don't need to update twice a week, you need to check the change log and see if there is something that is of major importance to you and only then upgrade.
I used last week's friday nightly build for my website Jan 18, 2013.. but since nightly build is updated twice a week - I will have to download and update everything week two times and do the same changes for branding on the new build ?
You should never change MonoX files directly (especially ones in MonoX folder), you should copy them to your location and then change them in order to be able to upgrade and not lose your work. If we do change something on those copied pages these are probably demo pages and you shouldn't worry about it. If we change some other functionality in MonoX Core and you update to nightly build it will be updated for you without any additional effort involved.
My another question is...for example I am using Jan 18, 2013 and you pushed a new build - there could be a chance that there are database changes / additions in new one - is it ok to skip any build ? or I can't ? since I am assuming the upgrade script takes updates the script from last build database and when any build is skipped, the sql server will throw an error if it doesn't find anything that was skipped since if new fields/tables were introduced in that skipped build are required for updating ?
In case you skip few, or whole month of, builds you should take a look at the DBVersion in Version table and then you go to the scripts folder in MonoX and start from your version up to the latest one in order to have a valid database scheme.
Or I can skip any build and use anu nightly build and when the installation screen is ON, I choose updating from previous version instead going with install as new database ?
No, there is no upgrade option in MonoX installation wizard, at least not that kind of upgrade. There is only an option to point MonoX app to existing database that you used from previous MonoX installation.