First question to the OP: What agency (i.e. PADI?) is your training course certified through? That will allow us to determine the exact standards which may have been breached. Once identified, those standards breaches should be communicated to the relevant agency, as a complaint. Most agencies have a Quality Assurance (QA) program that helps remediate and/or prevent negligence, unprofessional conduct or sub-standard training.
Question #1. Was this too soon and too little pool experience?
Your instructor should determine that, based upon your "mastery" of the skills taught in the pool/confined environment. If you cross-reference against your course manual, then you should identify each and every skill that
should have been taught and mastered in that phase of training.
Instructors (depending upon agency) follow a pre-set order of skills and dives. For instance, dive #2 cannot happen until confined water modules #1 & #2 are completed. Completion is not dictated by demonstration of the skills by the instructor, nor the repetition of skills by the diver... but rather by the
satisfactory performance of those skills by the student. PADI define this as "mastery". Other agencies have equivalent descriptions.
Check your course materials... they will help you identify exactly what you
should have been taught.
As a rule of thumb, a student that achieves 'mastery' in all the requisite skills should not need to ask the question you have asked. Aside from some natural anxiety about transitioning to the open-water environment and experiencing greater depths... it
should be self-evident that you were properly trained to make the progression.
Question #2. What is normal in terms of pressure on your ears? It was uncomfortable the whole time and I was trying to equalize pressure but never got there. Any tips?
You will feel some pressure. If a pressure differential didn't exist, then you wouldn't need to equalize. You should not feel pain though... not ever. As your ears equalize on descent, all feeling of pressure should ease. Your ears should feel no different to how they feel right now, reading this post....
Novice divers typically have more problems with ear equalization. Some interpret the feeling of pressure as one of 'discomfort', causing needless anxiety.
Equalize little and often, on your descent. Don't equalize too hard... that can cause as much pain/discomfort/injury as it seeks to prevent.
Question #3 did the instructor act like this because this is how they are taught to speak and act?
Instructors aren't taught how to speak and act. They are taught to teach.
There are bunches of bad instructors out there... same as there are bad, unprofessional individuals in any company or profession. There are also great instructors. The lesson to be learned is to be highly selective in your choice of instructor. The quality and safety of scuba training is largely determined by the merits of the individual instructor. Less so by the agency. However, the agencies themselves do vary in the quality and standards of who they accept, or how they train, their instructors. All agencies have some amazing instructors, some average instructors.... but some agencies have more useless dregs than others.
Question #4. Is it normal to have a little anxiety at first underwater?
Of course. Lack of anxiety would be more alarming!
Question #5. Is this good and I'm just anxious?
As an instructor, I'd much rather see a student exhibit some healthy anxiety. It helps to concentrate their minds upon improving their skills and help keep them diving conservatively...developing the challenge of their dives progressively over time as their confidence grows.
Over-confident divers can be a threat to themselves and others. They are the ones who tend to get hurt. Over-confidence is a disparity between confidence and ability... more often that not caused by an over-inflated opinion of your diving competency. It's easy to develop such an opinion when supervised and protected on a training course...and further post-course dives tend to reinforce that opinion because nothing goes wrong. However, a diver is only as good as they can perform
when things go wrong. That's when over-confidence is exposed. Sometimes that exposure leads to a close-call and re-evaluation of mindset. Sometimes it leads to people getting hurt.
Healthy anxiety is good and natural.
Unhealthy anxiety isn't. If you feel like verging on panic, or have excessive apprehension, then you probably need to reinforce your core training. Again, this is a mis-balance between confidence and ability. In this case, too little confidence based upon an under-inflated opinion of your diving competency. Panic is dangerous for scuba divers. Train sufficiently to have a level of confidence that matches your ability. That level of confidence should include a realistic assessment of your capability to deal with the emergency circumstances you were (or should have been?) educated about.