Does environment have any impact on a child's musical interest? What can parents do to create a musically rich home environment and communicate music as a priority to their youngsters?

When parents communicate that music is a priority, children make music a priority.
Parents can make time to share music. Sit down and share your favorite music with your kids…and start that process early. Go to shows, or just listen to music together from various time periods. Talk about what you are hearing, and what you like or dislike about it.

When do lessons begin? Can I start now?
Lessons can begin any time during the year. You can even start in the summer -- a great way to alleviate summer-vacation boredom!
Do you accept adult students? (Am I too old to begin piano lessons?)
Even if you have never studied music before, it is not too late to begin lessons. Often, adult students pick up the ability to read music in a relatively short amount of time. Lessons can be tailored specifically to the needs of an adult student, including lesson pace, materials, performance opportunities, and lesson time slots.
What piano method book do you use in your lessons?
For beginners: During the complimentary studio interview, the instructor asks questions to help assess what method book is most appropriate. Age, musical interests and prior musical knowledge are some of the factors that influence which method book is selected for a student. Right now students work mainly out of Robert Pace books and Celebrate Piano books.
With transfer students: Initially, transfer students are allowed to work out of the book they were using when they last had lessons. Due to the amount of new material in the Robert Pace books, that is usually what is given to in addition to the previous books.
The important thing is that lessons are tailored to each individual student's needs, no matter what method book is used, I will supplement  music worksheets, pieces selected from other method books, and sheet music that the student helps select.
What is the format of a typical lesson?
Beginners - Early-Intermediate: During a typical 45 minute lesson, a student will play pieces assigned the previous week, will learn or review a new skill or concept, and will begin a new piece or pieces. Other activities may include computer activities (music theory games, ear training, composition), rhythmic exercises, flash cards for notes and musical symbols, playing by ear, and improvising at the piano. The pace of the lesson will vary from student to student, depending on age, ability, and lesson length.
Advanced: Advanced pieces are generally longer and more complex, requiring  more lesson time for playing and discussion. Sixty-minute lessons provide the flexibility needed for learning these longer pieces and still allow time for ear training, theory, and composition activities.
How often would we meet for lessons?
Lessons are given weekly. Your lesson time will be for the same day and time each week, with the exception of planned studio holidays, group lessons and during your summer vacation. School age kids will have a monthly group lesson to share the music they are learning, learn various musical concepts together with other kids of similar skill and age.
I would like to purchase a piano. What do I need to know?
Please refer to the Piano Technicians Guild. These are the real experts and they can tell you everything you need to know about selecting and purchasing a new or used piano. When looking at a used piano, have a technician fully inspect it before you agree to purchase it. Good luck in your search!
I talk with a lot of adults who took music lessons as children and now regret they didn't work harder and stick with it. Some of those parents have their children in music lessons with the hope their kids will do better than they did. I'm sure you hear this a lot as well. What sorts of things can parents do to support and encourage their children's musical interests?  
There is a lot the parent can do. If the child is very young, sit in on the lessons as the instructor permits and ask questions so you can reinforce instruction at home. That is quite valuable to the child's progress. The young students (under 10) who tend to quit are the ones who have parents who are very passive in the learning process. If the parent doesn't value the instruction enough to get involved and make it a priority, then the child won't value it.
The parent can plan on a weekly concert given by the child. This provides regular reinforcement but also gives incentive to the child to be ready to play for mom and dad and others.

If the parent can't play, the parent can ask the child to teach them what they have learned about instrument. This actually causes the child to organize the information better because they now have to communicate it to another person.
Performing or playing the piano (ie: for 1-5 older people who appreciate it so much, for church, or to a big crowd somewhere, etc) where the child is receiving much positive feedback is helpful at all ages. Incorporating the piano playing with other kids will provide positive peer interaction.