Sql-server – Manual failover of AAG in SQL Server 2012

Can I related the crash to availability mode settings?

No. By the looks of your log messages, you actually lost cluster quorum due to the removal of two nodes' votes, and then your witness (file share). Is this a 3 node cluster with a file share witness perchance? In that case, if you pulled these events from one of the node's event logs, then it may appear to each of the nodes that there is a lack of communication with all voters. That would generate a similar, if not same, error footprint like you have above. Nobody can talk to anybody, if that is the case.

During that time, the quorum will be lost as you are currently seeing. There is a level of assuming here, as I'd need to see way more diagnostic information to pinpoint the cause of voter removal, but that is why the quorum was lost.

Regardless, this appears to be a problem that surfaced in a down cluster, in which case your availability mode would have nothing to do with the WSFC cluster failing.

As for "best practices" for the availability mode to go with, you need to determine requirements for data loss, performance impact, and a few other factors that are best described in this BOL reference on Availability Modes.

The only group that failed over was the Available Storage group, which you aren't using, so it is something you can just ignore. If you want to increase the number of missed heartbeats that will cause it to fail over, change the SameSubnetThreshold accordingly.

(get-cluster).SameSubnetThreshold = 15

See Clustering and High-Availability for details.