"in the last weeks" or "over the last weeks"

[Englishnow]

Future

I'm going to travel next week.
I'm going to travel for the next weeks/week.

Is there any variation depending if "week" is plural or singular ?

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Past -> Until now

I've been working over the last week.
I've been working over the past week.
I've been working in the last weeks/week.

To mean "throughout", the beginning of the action until now, which of those sentences above are right ? I also got a little confused about "last" and "past" concerning those situations. In addition to it, when the noun week is in plural or singular, is there any change in the structure ?

Thanks in advance.

[Mister Micawber]

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Is there any variation depending if "week" is plural or singular ?-- In meaning? Only the obvious one of length of time.

To mean "throughout", the beginning of the action until now, which of those sentences above are right?-- The first two suggest this more strongly.

In addition to it, when the noun week is in plural or singular, is there any change in the structure ?-- See above.
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Native English teacher at Mister Micawber's