Which country is better for M.Sc in engineering management: UK or Germany?

It is smart to have backup  plans. Apply to several universities and not just one. Getting into your top choice isn't guaranteed because many students apply and competition is tough. Having other options saves you time and stress if your first choice says no.

The UCAS applications for the UG courses in the UK open in the month of May. While the deadline to submit the applications for most colleges and universities falls on or around September 03. Deadlines for the University of Oxford and most courses in medicine falls near October 15.  

The earlier you start preparing for the fall intake in UK, the better. Get your test scores, documents, finances and other related requirements ready well before the admission applications commence. You must start at least 15 months before the desired intake. You should also be prepared with complete information on your finances/scholarships/loans.

No, the Chevening Scholarship is awarded only for taught master's programs in the UK. The research-based master's programs (such as MRes), PhD and DPhil are ineligible for this scholarship.

There is no official requirement to resign from your job. You have to be available for receiving scholarship award. Talk to your employer in advance.