A: Electronic signatures are generally legally valid and enforceable in most jurisdictions, but the specific enforceability of your stock subscription agreement depends on several factors: a) did you have an intent to sign b) were securities laws followed in this offering. You'll want to engage a litigator with experience in these topics, esp. securities laws.
A: Generally when you leave a job you forfeit all rights to unvested stock options since those "vest" or "become yours" based on time worked at the company. If you have any stock options that have vested based on your work at the Company, those may or may not be forfeited depending upon what your Stock Option Agreement says. Please review that carefully or hire a lawyer to assist you to advise on next steps.
A: Make sure you respond to the letter and meet any deadlines required. You can respond as you have here that you do not think you have infringed on their trademark. Call them and try to work out a solution. If you can work with them to reach resolution, that will be much easier. If this becomes a lawsuit, unless one side settles, the case will take a long time and have to go all the way to trial to decide if it is infringement. It's likely that the legal fees will get very expensive. You should seek legal counsel if you believe that is within your budget.
A: This is an important distinction and has both financial and legal implications. Independent contractors do not get overtime, benefits or workers compensation and thus are generally cheaper to hire and easier to fire than an employee who does get these benefits. The IRS and Department of Labor use multi-factor tests examining control, financial aspects, and the relationship's nature—key indicators include whether you provide tools/equipment, set specific hours, integrate the worker into your business operations, or maintain an ongoing relationship versus project-based work. Given the complexity and high stakes of worker classification in the tech industry, where the line between employee and contractor is frequently blurred, I strongly recommend consulting with an employment attorney who can review your specific situation and help establish proper classification procedures. Additionally, consider having workers sign clear agreements that reflect their true working relationship and maintain documentation supporting your classification decisions.