The state "license" is obtained when you incorporate with the Secretary of State. You will also need a business license from either the county or city where the business is located, depending on whether you are within the city limits or in unincorporated county.
You should be concerned, but there is no way to tell you whether you are in fact infringing on their trademark, or if they even have a protect-able mark. Such things are very fact-specific. Retain a local intellectual property attorney to discuss and gather all of the facts to decide next steps.
No, not properly. If the company has any outstanding debts/monetary obligations, it is not proper to dissolve the company. Doing so can lead to personal liability for the individual dissolving the company. However, you should discuss this with the attorney assisting you with the tax issue. For example, if you already have personal liability for the tax obligation, it may not ultimately make a difference.
Names used in commerce automatically get trademark protection (assuming they otherwise qualify as a proper trademark). You do not need to register the name to protect it, although federal registration may make sense at some point. However, you should make sure the name will be a proper trademark before investing resources into it. Retain a local business and intellectual property attorney to help you.
Your situation is not uncommon, but can be very complex if your partner is not willing to voluntarily transfer her interest to you. If she is willing, she would transfer her stock/membership interest to you via a purchase agreement. Then, you would attempt to amend whatever contracts she is a party to. However, keep in mind that the other party to those agreements may not be willing to allow her to be removed.
If she is not willing to give up her interests, the situation becomes too...
It really depends on many factors. Generally, an LLC is the better choice for a small company because of its flexibility, but not always. Retain a good business attorney to discuss your situation and advise.
I agree with my colleagues' answers. I will add that an operating agreement is not required for an LLC in Georgia, although always recommended. If you do not have one, the rules of the Georgia LLC Act will apply, which I assume you have never even looked at it. Therefore, I always recommend a customized operating agreement even for a single member LLC. That way you can keep it simple and straightforward.
Other than filing for bankruptcy protection, there is little, if anything, you can do to avoid liability regarding the lease since you personally guaranteed it and there is already an issue of collection. In other words, it would be fraud if you transferred all of your personal assets to avoid the rent obligations. Your best course of action is to retain an attorney and negotiate a termination of the lease.
However, there are other ways to protect your personal assets moving forward, such...