Can I kill these MSCRM related SQL processes?
The SQL backups have been failing for a few days... I tried to just do a quick manual full backup and got an error: 


It seems like operation which conflict with backup are running at the time which backup was started so the backup failed. And as per your comment SPDI 186 is running which is showing backup which means that database backup is already running when new backup was being started. Concurrent full backup is not allowed when full backup is already running.

Also make sure no database shrink operation is running or Auto Shrink is not enabled. This can also interfere in backup operation.

select is_auto_shrink_on, name from sys.databases 


let us see how many databases have auto shrink enabled

Yes you an kill backup operation (SPID 186 here) but you would loose all the time spent in taking backup and you would have to start all over again. Before doing that let us see how much backup has finished, what is output 

select percent_complete,session_id,status,total_elapsed_time
from sys.dm_exec_requests where session_id=186


EDIT: There is NO restart required

Edit:

After discussing on chat it was identified that Veeam backup was running for past 2-3 days and was somehow hung. OP killed the process and it went into rollback state where it was again stuck OP has to ultimately restart the VM and the issue seems to have resolved.

Also advised OP to log a ticket with Veeam because that was definitely a third party Veeam backup issue.