We have a live magento site with version 1.7.
In a dev installation (magento 1.9) , we had put a snap of live site database.
In dev site, we have changed theme, we have added some extension and we have done some other changes.
While we worked at dev site, in live site we have added products, we have had sales, more customers added etc.
How we can update dev database (with new products, new customers, new sales from live site database) without losing other changes we have made in dev site?
That's always something that's pretty difficult. First of all, why do you need this new products on live to be in the dev environment as well? Your live database will still be the database you'll be using when you put the upgrade live. You don't want to lose orders and customers that were added to the live environment but don't exist in the dev environment.
I personally had to do some migrations in the past few years and what I always do is make a plan that I have to follow when putting the upgrade live. This plan contains stuff like "put site in maintenance mode", etc. But it should also have a "run installer script" section. And those installer scripts are the ones I really like.
To install data like CMS pages, updated category descriptions, etc. from the dev environment on the live environment, you could use these install scripts. In these scripts you can add the raw MySQL queries you want to run. It will require a small custom module, but that way you can install the data by just one command in your command line and have your data available in no time.
Another advantage of this approach is that you can test your installers all the time. Just create a new copy of your live database on your local environment, link your Magento shop to that database and run your install scripts locally. If it throws an error, you can fix it and if you find out you're missing content, you could just update the installer script and retest it.
I've used this article as a guide for making installer scripts: http://inchoo.net/magento/using-magento-1-6-data-install-scripts/