Setting up a tea garden

Hi Valerie,
My wife and I would like to set up a tea garden.  We have a beautiful peaceful large front and side garden, a field to park in and we have outside toilet facilities.  We are not near main roads.  There is a house approximately 150mtrs along our track but no one lives in it.  The farmer that owns it comes occasionally to cut grass etc and feed his sheep. Apart from that, we have no neighbours at all.  We would have wooden picnic benches with umbrellas and it would probably be seasonal, mainly Sunday’s.  We would like to offer tea, coffee, hot chocolate, soft cold drinks and home made cakes.  My wife makes the cakes.  Can you tell us if we can do this at our home using our own kitchen?  We have animals too… horses, ducks, chickens, sheep, one soppy golden retriever and two cats.  My wife is a registered Esthetician of 15 years and we run a gite too using the auto-entrepreneur system.  My questions to you are:

1) Firstly, are we allowed to do this from our home?
2) Would my wife be allowed to make and sell her cakes as she has no catering qualifications? 
3) Presumably there is a Health & Safety inspection required?
4) Are we allowed to open on Sunday’s?
5) Would this activity be added to the AE system that my wife already has in place?

Many thanks and we look forward to the reply.