Given company's products that promote work from home - the company as a whole is flexible for most team members. However, it can be at your individual manager/director's preference whether or not you can actually work from home. It is luck of draw as to which personality/philosophical view your immediate manager has.
Not only allowed, but required - they want you to work 24/7.
Highly team dependent, but most teams accept or actively promote occasional work from home/anywhere. Some managers treat this as a perk that needs to be earned. Remote work arrangements on a permanent basis are almost always a career derailleur. No senior manager or leadership wants a remote employee, especially in Engineering.