In fact there were Trustees appointed after Nigel was murdered. Lizzie is not one of them. In theory she can do nothing at LL without Trustee approval. Scriptwriters consider this impossible apparently, hence the bedrooms which went directly against the agreement with Gay Grables when LL started up.
Freddie is the named inheritor as the son – but I am not sure when he inherits – it could be 25 as Nigel did not inherit at an early age.
Rovers is 50% Lilian, 45% Jolene and 5% Jamie if I remember correctly – not sure that Meriel gets a look in as I am not sure Jolene sold any of her share to Kenton.
Home Farm is a mess – the latest attempt to put things straight was a total nonsense with Brian apparently conceding control – something he would never do.