My experience on EK 772 and 773 aircraft is No (recline), No (pajamas), and No (special bed linens).
The First seats have nice footrests but hardly recline at all. Less comfortable for sleeping that many business class seats on other airlines.
Their real claim to fame is the in flight entertainment, which has giant screens in First and many interactive features.
I found in flight service on overnight flights much too intrusive during sleeping times. On day flights, it is fine.
I've decided to take my business elsewhere even if it means business class instead of EK first.
Charles