Q1. Can the numbers indicating that there were over 370k nodes be trusted?
Yep. Reasons have been given before.
Q2. Why was there such a sharp fall in numbers? GPU and then ASICs?
No. Mining had (almost) nothing to do with it. Although that might have contributed, since miners were likely to run full nodes as well. With the concentration of mining, you'd expect a concentration of full nodes as well.
One of the reasons were obviously lightweight wallets.
But most probably the most important factor was a redefinition of how those numbers are estimated. I guess that the ~6000 nodes today only take into account the more or less permanently running nodes, whereas the old numbers also counted nodes that were only connected infrequently. But that's just a guess, I'm unsure how bitnodes.io counts.
Q3. Is is possible to ever see that number again?
Unlikely. But a stable number above let's say 10.000 would probably be nice to have.