Gosh asking how long the ASICs are taking to process is akin to asking how long is a piece of string
The wait has been up to 8 weeks, since they have a HUGE backlog. I would suggest that 5-6 weeks is about normal at the moment.
As for training dates, there aren't any scheduled to my knowledge, however aviation is a rapidly changing industry and Eastern often puts on training schools at short notice.
Having said all of that, Good Luck and congratulations

SG