And you want all that for free here so you don't have to hire an attorney like you should, right? Maybe, probably, both but mostly you, no, both, no it makes butter the owner and claimant, and liable for what? Is you want explanation hire an attorney like you should have already.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
Attorney Burdick is right - you're asking for a full-boat analysis of your legal rights and risks when commissioning artwork for commercial purposes. Only your own attorney can do that analysis after reviewing all the facts -- including those that you don't think are important -- and reviewing the business dynamic in which the art will be purchased and in which it will be used. Conclude that this analysis is not "profound" if you like but if just one thing goes wrong it is often people with your mindset that are first to blame the lawyer and, sometimes, to sue. So, like doctors performing defensive medicine, attorneys must protect themselves from their own clients. Which, in this situation, is to NOT shoot from the hip with answers to your six questions.
The only appropriate response is that the artist and the hiring party can, by contract, agree to whatever they want. Including who owns the copyright, who is responsible for responding to infringement claims, and the scope, if any, of the warranty by the artist and his indemnity obligations. And even if an agreement is reached on all issues, the attorney needs to evaluate if any of those promises mean anything as a practical matter.
Speak with your own intellectual property attorney. Good luck.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
Sometimes the law (either a statute or case law) provides an easy answer to a question. Sometimes it sets up a test or a series of questions that have to be answered in order to determine what the legal result is. This is a situation in which there are a series of fact specific questions that need to be asked to determine whether something is a work made for hire owned by the customer and a work that will be owned by the artist.
Honestly, this something where you have to discuss the facts with an IP attorney to get an answer that is worth anything.
This question cannot be answered without reviewing the agreements between the parties. In general, however, independent contractors maintain ownership of the works they create unless there is a written agreement that assigns them as works for hire (or otherwise) to the person or company which commissions their work. It is the person who creates the design who is entitled to the copyright---a company that merely instructs its people to follow the instructions of the designer is not a co-owner of the copyright merely because it carries out the technical tasks associated with implementing the design. However, if both parties contribute to the development of the designs, they could be deemed co-authors. If the parties are co-authors, the prohibition on infringing works of third parties would not stop either of the parties from licensing or exploiting the works they jointly created---however, whichever party exploits the work by licensing or using it will have to account to the other party for an equal share of the profits or revenues that are earned from using the copyrighted design.
This is a very common problem because many companies make the mistake of working with independent contractor/providers without having written agreements that clearly address the ownership of intellectual property. It never ceases to amaze me at how seemingly intelligent business persons make the mistake of operating without proper legal counseling, including most importantly, intellectual property counsel. The mess you seem to face arises from the fact that the agreements were poorly drafted and did not involved advice of IP counsel. These problems become particularly acute when the provider and the person who commissioned the work have a falling out or terminate their business relationship---and then the provider quite correctly can claim that it is a co-owner (or more likely the sole owner) of copyrights in the designs that he created.