No, in fact, it is not.
Concerning The Sims 3, at the very least, it is stated in their End User Licence Agreement, in section 2, subsection B, paragraph 4, that:
"In exchange for the right to use content contributed by other users through the Software, when you contribute content through the Software, you expressly grant to otherusers of the Software the nonâ€exclusive, perpetual, transferable, worldwide, irrevocable right to access and use, copy, modify, display, perform, and create and distribute derivative works from, your contributed content in connection with the Software, and to distribute and otherwise communicate your contributed content as a component of works that they create using the Software, for example, The Sims lots or The Sims videos, without further notice, attribution or compensation to you. You hereby waive any moral rights of paternity, publication, reputation, or attribution under applicable law with respect to EA's and other players' use and enjoyment of such content contributions in connection with the Software." [Emphasis mine.]
As The Sims Resource charges a subscription (as of this writing) to access some of their content, they are in violation of the EULA and thus infringing on EA's intellectual property rights.
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You must have the sims launch open, and the hair/whatever, must be installed on to the sims. Also, you must be logged on in your launcher!
custom content is legal for the sims 3 and any other game,unless it breaks copyright laws
No. Modding is allowed in the game and as such you are free to download anything you may find interesting from the website.
You can only do this if you download naked mods (modifications) off of Sims download sites, like modthesims.info. These sites are legal, and are endorsed by EA (the company that owns The Sims Video Games).
The only legal way to download The Sims 3 Island Paradise is to buy it through Origin and then download it from there. Any other way would be considered as pirating and that is illegal.