I can’t offer much advice on the alone training because it is not something I have had to deal with, fortunately! I do agree with Clare that he has been with you a very short time and everything is still very new. Also, at 1.5 years old he is still really a puppy. He won’t grow bigger physically but mentally, think of him as a teenager, not an adult .
The reason general wisdom says to not leave greyhounds outside is that they have little body fat and usually thin coats, so they don’t adjust well to temperature extremes. Most greys seem to be more tolerant to cooler temps that hot, so be very, very careful about leaving him outside in the summer, even with shade and water. And by hot, many greys consider anything over the low 70’s (F) hot! That said, many of them like to go and lay out in the hot sun and bake, and greys we get from the farms have spent a lot of time outdoors and have heavier coats. I hope this helps clarify some of the “is it ok to leave him outside”.