Your query: Is it legally allowed to use other company's name in my company's advertising slogan?
Response: Maybe, maybe not. If your tag line is "The Best Buy In Wheelbarrows Anywhere" Best Buy, Inc. could not prevent you from using its trademark "Best Buy." If your tag line, however, is "Canon Copiers Can't Compete" then Canon, Inc. could bring a claim under trademark law for dilution and false advertising.
If you intend to use another company's trademark in your advertising then you NEED to discuss the matter with an intellectual property attorney.
As for your "some restrictions apply" inquiry, it sounds like you intend to publish an offer knowing that you can't satisfy the reasonably expected consumer response. The short answer is that stating that "some restrictions apply" will NOT make your offer lawful. You need to make clear in your ad that the goods or services being offered are in limited supply ("only ten available at this price" or "this price available to only the first ten customers").