I'm a Production Manager at a fence company in Austin so I'm able to answer your questions and give some advice. As mentioned above, you can ask the neighbors to split the cost but don't count on it. 99% of the jobs we sell are to just one buyer. Rarely do they split the cost of replacing the fence.
This is very good advice. It'll make it easier to communicate your wants with your estimator. It'll make it easier to ask specific questions if you're just talking about 1 style of fence rather than asking about multiple fence types. In my option, ask for round steel posts as they will last much longer than your wood fence will last and you can reuse them in the future. Go with Western Red Cedar rails and pickets. We also offer treated rails and import cedar pickets but they don't last as long.
Yes, under Texas residential law you must have a fence enclosing your pool. It must me at least 48" tall. The gate must be self closing, open outward and the latch must me at least 54" above the ground.
Some advise. Make sure to inform all your neighbors of the project ahead of time and the day before even if they are not splitting the cost. As an install company there's nothing worse than going to a job and we can't start because a neighbor's dog is loose in their backyard because they weren't informed to put them in the house or tie them up.
Its standard practice to remove the old fence and install the new posts on the first day and return the following day to nail up the rails and pickets.
Usually the fence company will submit the request to 811 on your behalf but verify they came out to mark all underground lines (gas, electric, phone, internet) before the work is to start. They can't locate water main lines or sprinkler lines unfortunately. Inform the fence company a day or two prior to starting if it hasn't been marked so they can submit a no response to 811. Being proactive will avoid delays starting your project. Let me know if you have any questions.