We have access to all the information on your account that you’ve mentioned. Without that, we’d simply be unable to do our jobs.
Yes, we have access logs - we don’t balance them against contact logs because not every check of an account happens in response to contact from the customer - there are all sorts of reasons why we might need to look into an account pro-actively, including financial crime reasons, people affected by fraud rings, people who might be identified as being affected by bugs, people who might have reached out via other third party means, ongoing issues that we need to check over time (not just as a one-off) etc.
Regarding privacy screens - COps within the office work in a secure area where visitors are not allowed. We have provided privacy screens for people who regularly work outside of the office. That said, if a random person were to see our screens, they wouldn’t learn much without understanding our interfaces and what each area of our backend support UI represents. It takes quite a bit of training just to teach us what everything looks like and how everything works in relation to everything else, so if you hadn’t gone through that you would quite frankly be quite lost! We have a strong culture of locking our screens whenever we’re away from our machines and if you leave your machine unlocked in the office and someone notices you will be made to purchase donuts for everyone as compensation 
I don’t know the technical aspects of MDM but we’re able to remotely wipe a device should it get lost, for example.
Alerting the customer that their account has been viewed is not only a very bad idea, but it’s also illegal under “tipping off” regulations. It is against the law to provide a user who is suspected to be engaging in financial crime with any reason to believe you might know about their activity, in any way shape or form. This obviously still applies even if there are false positives and it ultimately turns out there is no financial crime happening.
Ultimately it comes down to you trusting us as your financial provider, just as you would with any other bank or service. Getting a job at Monzo requires a high level of vetting and trust from the company to us as a member of staff, and part of that trust is to not do things that would in any way damage the company or it’s customers - I imagine this is a similar culture to Facebook or Google, who know much more about all of us than a financial company would!
Hopefully that answers all of your questions! 