Are these statements enough to prevent a content owner from successfully suing dribbble.com?
Such statements in a ToS or user agreement are helpful, but will not, standing alone prevent a suit for copyright or trademark infringement against the site.
First of all, it is possible that simply uploading an image or other content infringes the copyright, if the user had no right to copy it (uploading involves making a copy), even if the content is never downloaded. The quoted warranty from the user does not even mention having sufficient rights to lawfully upload.
Secondly, it is not enough to request that users state that there are no rights being violated. Such a policy must be enforced by the site operator. 17 USC 501 (a) provides that:
Anyone who violates any of the exclusive rights of the copyright owner as provided by sections 106 through 122 or of the author as provided in section 106A(a), or who imports copies or phonorecords into the United States in violation of section 602, is an infringer of the copyright or right of the author ...
The exclusive rights listed in 17 USC 106 are: (1) The right to make copies; (2) to prepare derivative works; (3) the right to distribute copies; (4) the right to perform the work; (5) the right to display the work publicly; and (6) the right to perform the copyrighted work publicly by means of a digital audio transmission. Any upload without permission from the copyright holder would violate (1). Hosting a work without permission would violate (3) and perhaps (5) or (6). If fair use applies to an act, it is not infringement; see 17 USC 107. 17 USC 106A sets out the author's "moral rights", which in the US apply only to "works of visual art", including drawings and photos. Sections 107 through 122 mostly deal with limitations on these rights, or restrict the scope of specific rights, or provide for compulsory licenses (permissions).
If a work is uploaded or hosted without permission from the copyright holder, then at least one of these sections will apply, and the uploader and the site operator might be successfully sued for infringement.
However, under 17 USC 512 (c) an online provider:
shall not be liable for monetary relief, or, except as provided in subsection (j), for injunctive or other equitable relief, for infringement of copyright by reason of the storage at the direction of a user of material that resides on a system or network controlled or operated by or for the service provider, if ...
- does not have actual knowledge of infringement;
- does not have knowledge that makes infringement apparent (good ground for suspicion);
- On learning of actual or probable infringement "acts expeditiously to remove, or disable access to" the infringing content;
- does not receive a financial benefit directly attributable to the infringing activity;
- On being notified properly of a claim of infringement, "acts expeditiously to remove, or disable access to, the material that is claimed to be infringing" 17 USC 512 (c)(3) spells out in detail what a notice must contain to be "proper". Getting such a notice makes the provider legally "aware" of claimed infringement.
- maintains a designated agent who can be notified of alleged infringements. Contact info for the agent must be posted on the site and filed with the US copyright office.
- announces and reasonably enforces a policy under which subscribers and account holders who are repeat infringers have their accounts terminated (17 USC 512 (h));
If a provider does not comply with any of these requirements, that provider may lose the "safe harbor" status, and be subject to copyright liability. A provider is not legally required to comply, but not doing so puts the provider at risk of a successful suit.
The provider might be able to sue the user in turn under the user's warranty quoted in the question for reimbursement, but copyright damages can in some cases be quite large, and there is no knowing if the user would be able to cover such a claim, even if a suit under the warranty was successful.
Copyright and trademark infringement are torts in most if not all countries. A copyright owner may sue in any country in which the copyright is infringed. The above safe harbor provisions are specific to US law. Many but not all countries have somewhat similar provisions, but the details will vary. Complying with the US provisions may or may not satisfy the requirements to avoid liability under the law of some other country
If the uploaded content includes a protected trademark, and it is used in such a way as to benefit from the reputation of the trademark product or service, or so as to confuse potential customers as to the source of the content, or so as to falsely imply that the content is approved, endorsed, or sponsored by the trademark holder, the trademark holder may have a valid action for trademark infringement. The safe harbor provisions listed above do not protect against trademark infringement suits.
Trademark laws, like copyright laws, vary by country, and a mark protected in one country may not be protected in another.
However, using a trademark to refer to, or as a name for, the product or service the mark is associated with, is often held to be nominative use, which is not an infringement.
The language quoted in the question will in no way immunize the provider from a valid trademark suit.