Can I say "In order to work this all" instead of "In order for this all to work" here?

Can I say "keep watching" instead of "keep watch" here?

Excellent question. "Keep watch" is an idiom. It means to observe with continuous attention, especially as an act of protection, which is what the police officer is doing here. To "keep watching" means to continue watching/looking at something, for example, a movie. Ex: The bird keeps watch over her eggs. Ex: Do you want to keep watching this?

I've heard that many countries in Europe have their own nobiliary particles. Like "von" for Germanic nations or "de" for French so on and so forth. But, I don't think either the British royals or aristocrats use the nobiliary particles for their surname/title. Why is that?

England and Wales use the particles "de" or "of." "Of" is the more common one. For example, Prince Philip was known as "the Duke of Edinburgh." Or Meghan, "Duchess of Sussex." However, other uses of "of," like, "Richard of Shrewsbury" is used less now. The particle "de," which was borrowed from Latin and French when used in England and Wales, isn't used much either. So I suppose it either just went out of fashion or became less important to have these titles as time went on. Ex: There was once a "Simon de Montfort," Earl of Leicester. Ex: Prince Louis of Cambridge is such an adorable child.

Is "UPD delivery service" really exist?

I don't believe so. I think it is a fictitious delivery service that the show made up. I do not live in the United Kingdom, but after doing some research, it doesn't seem like this service exists.

Does “be obsessed with” have a negative meaning?

Not always. "Being obsessed" with something means that you really like something. A person can be obsessed with music, food, animals, etc. It just depends on how the obsession affects your daily life. An obsession is usually considered negative when it negatively affects your daily life. Ex: She's so obsessed with him that she's stopped hanging out with her friends. Ex: He's obsessed with going to the gym.

What does “beat your butt” mean?

"Beat your butt" here is an expression that means to defeat someone or win in a competition. Usually, the more common way to say this is "kick your butt". Both "beat your butt" and "kick your butt" are nicer ways to say "kick your ass", which is also very common. Ex: He beats your butt in the race. Ex: We are going to kick the other team's butt in the soccer game today!