No. In British parlance these would be called East Asians hailing from east of India.
No, it includes those from India as well - a significant proportion, in fact.
Historically, the US Census had put ‘East Indian’ as ‘Caucasian’ until it was changed to ‘Asian Indian’ in more recent times (70s?). So, many studies and surveys that categorise ‘Asian’ also included Subcontinental Indians.