Most piano teachers teach classical piano including sight reading, music theory, and maybe a little music history. Not much attention is given to good playing technique, but these form the core of a "classical piano education." I teach these things, but add a strong emphasis on developing a technique that will carry the student into advanced playing as soon as possible. However, I believe that if the education stops here, as it often does, a person becomes "half a pianist"; able to play anything if the music is in front of them, but completely unable to create, compose or play without the aid of written music.
There are some pianist out there I like to call "jazz pianists." They can play lots of cool things, but if you put a piece of music in front of them, they can't play it. These people almost never teach piano because they don't want anyone to find out that they can't read music. These people also fit my category of "half a pianist." When I was young I thought that only a few super talented prodigies could play by ear and improvise. It wasn't until I started the doctoral program at Juilliard that I realized improvisation could be taught, and that no super talent was required. I have now been teaching the skills of improvisation, arranging, transposing, composing, and playing by ear for the last 10 years with great success. I love that my students now can become full pianists, possessing the full set of practical skills called upon in musical settings.
With classical music reading, theory, history, technique and composing, transposing, arranging, improvising, there still remains one crucial element needed for a full music education at the piano. I will call this "musicality." It is the ability of the pianist to move their audience. It is not enough to just play the notes on the page or make up a series of notes and chords that sounds good together. The pianist must tell a story, communicate an emotion, paint a picture, all with abstract sounds. This is the chief aim of all music; to communicate. Sometimes it is in getting the audience to tap their toes, sometimes it is to get them to feel sadness, joy, fear, or peace, but it always to get them to have some kind of response to the music beyond just hearing the notes. Over time, I strive to teach students how to play with great musicality and communicate wordless stories filled with emotion.
I have a very wide age range of students. My youngest student ever was 3 years old. I would say that many 3 year olds and most 4 year olds can benefit from private piano lessons, but the expectations on progress must be reduced. Simply put, a 4 year old does not progress with the same speed as an 8 year old. However, I'm not saying wait until the child is 8. An 8 year old with 4 years of lessons under their belt will always be significantly ahead of the child waiting until age 8 to start.
Though my oldest current student is 78, I have had students well into their mid 80's. I love working with seniors who are brushing up on skills from the past or are finally getting around to pursuing their lifelong dream of becoming a pianist. Since I teach full time, I can accommodate the scheduling needs of retired persons.
For beginners, I usually have 45 minute lessons. This gives us enough time to fully debrief the previous weeks material, and dig into the new assignments together. 30 minutes is just not enough time to hear the prepared material, fix any problems, answer any questions that come up, listen to any original or experimental work the student has done, and fully prepare them for the next weeks material, teach them how to practice, introduce new concepts, and cover problem areas that might come up during the week. Advanced students and those seeking an accelerated rate of progress and challenge often take longer lesson lengths.
Group lessons are not a good idea, unless used as a temporary strategy to get several students from the same family into beginner lessons. Sometimes schedule or financial concerns can cause us to need to start things off in this manner, but it must always be looked at as a circumstance to be changed as soon as possible. Students simply move at different rates, and within a short period of time are on very different planes of playing.
A person cannot learn piano without having access to one. A piano has a soul and a keyboard is a computer. A piano is a far superior instrument to a keyboard. That being said, I think it is totally unreasonable to expect a family to invest in a piano when they don't even know if the student will stick with it. Therefore, when we start lessons, I will use what ever the instrument the student has. I will help the family evaluate their instrument and see if an improved instrument is needed, and at what point in the future it will be needed. I always advise and offer free assistance in helping my students obtain an instrument of the highest possible quality within their budget, when it comes time to upgrade. However, you do need something to practice on within the first 3 piano lessons, whether piano or keyboard. A person cannot learn an instrument if they do not have one.
When a student first starts to study piano, not much time is needed to complete the assignments. Over the first few months, the time needed gradually increases. Each person is unique, but I have noticed over the years of teaching, that students who shoot for 3 hours of practicing a week, and never let themselves get below 2 hours of practicing during the busy times, experience positive progress and are generally prepared for lessons each week. Now, I have students who practice much more than that, and piano is something that ... you get out what you put into it ... but in general, students who practice 3 hours a week are happy with their progress. Advanced students must spend more time than this to see continued progress.