Reiki is not a substitute for medical treatment.  Reiki practitioners are not licensed to diagnose or treat health conditions.  Reiki works to balance the system energetically and support healing and, as such, works best when used in conjuction with other forms of treatment.

No.  While you are probably moving energy -- we all have this ability to one degree or another -- Reiki is a specific system of accessing Universal Life Energy.  It is not the energy itself.  In order to do Reiki one needs to be attuned by a Reiki Master and trained in the system.

Most do.  Some don't.  I have found that horses, dogs and fish tend to love it.  Cats are more variable.  I'm told birds are very receptive, although I have never personally done Reiki with birds.

No.  While many people who practice Reiki are religious, they have nothing to do with one another.  Reiki is simply a system for moving energy.  It is compatible with any religion -- or none.  There are 5 precepts that provide guidelines for living that many practitioners follow.  These, too, are compatible with any religious practice.

Not necessarily.  In my experience, it matters more that a person is regularly using their Reiki than what level of training they have received.  A First Degree practitioner has everything he/she needs to give an excellent treatment.  The more a person practices, the more familiar they are with the energy and it is easier for them to discern when they are blocking or getting in the way and they can adjust as necessary.

No.  While some healing modalities allow for the taking on of others' ailments, Reiki offers a natural protection.  Because we, as practitioners, are simply channels for healing energy we are not in a position of taking on anything.  We are simply moving energy.  And, as the energy is moving through us, we also receive the benefits.

No.  There is specific training on how to do distance healing in the Second Degree course, giving people information about the many ways that can be done.  However, that training is not necessary to be able to send Reiki over time and distance. 

Many people stop with First Degree training.  With that, you have all you need to do a Reiki treatment very effectively.  Second Degree training provides tools to help people focus their gifts more fully.  For people who want to make Reiki a bigger part of their lives and actively practice, it can be useful.  It doesn't make the Reiki more effective, it simply gives you a bigger toolkit to draw from.

The reason to do Master training is if you want to make Reiki a significant part of your life and you want to teach others.  In my opinion, Master training is much more than a simple attunement.  It is a long-term learning commitment that one makes with their Master.  I maintain a close connection with my Master and consider this a very important part of my practice.  It is a very rich and rewarding relationship that continues to challenge me, and consistenlty invites me to grow.