The answers to your questions are found in the question and answer section of the Texas Secretary of State's website in the business section--amendments and corrections FAQS.
You do not need to file an amendment to the certificate unless you are actually changing something in it. You are not required to file an amendment to change a director. To change the registered agent, there is a simple form on the Texas Secretary of State's website that you file with a small filing fee of $15.
Although you probably don't need an attorney to handle the change of registered agent, it may not be a bad idea to retain an attorney to help with the transition, in general.
The above statements are provided as general information and not intended as legal advice. Each matter has its own set of unique circumstances that cannot be adequately addressed without consultation. You are strongly advised to hire an attorney licensed to practice law in your state to represent you.
File and updated Public Information Sheet with the new ownership. File an agent change form to change the registered agent. You may want to have an attorney help, because filing an agent change form incorrectly leave you without an agent which is a violation and grounds for revoking your entity status. This sort of error is usually uncovered once you are sued, and it is too late to fix it then.
I am an attorney licensed to practice in Texas, Louisiana and before the United States Patent and Trademark Office. Laws vary from jurisdiction to jurisdiction and the above may not be an accurate assessment of the laws for your area. The above should be taken as general guidance and not specific legal advice. For specific legal advice you should seek a licensed attorney in your jurisdiction practicing in the area specific to your issue. The above does not constitute or establish an attorney client relationship. If you wish to receive specific advice about your legal issue, then contact my office to schedule a personal consultation.