1. - Hello George. Don't think that I forgot to prepare you research (i.e. I didn't forgot I am working on it now)
(a) Не думай, что я забыл ...
2. I preferred to sent you an e-mail rather than calling you because I wanted to avoid putting you in the difficult position answering immediately to my invitation.
3. I invite you to come in Cyprus during (this) winter.
(a) приглашаю тебя приехать на Кипр зимой.
4. I am inviting you to my wedding. I am willing to cover your residency, transportation, food expenses
(a) I want to avoid to word "pay". Я покрою твои расходы транспортации, жилья
5. I don't want immediate answer. Think about it.