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My friends, can anyone help me =)?

1) It is from U.S. constitution:

'he shall take Care that the Laws be faithfully executed'
Why "be faithfully executed'? and not " will be faithfully executed"

2) or another example (from internet):
It is important that the law be observed (again, why we use just 'be'?)

3) If the distance between the two points be the same, no further experiments will be necessary. (two points be the same?)

4) Be it ever so humble there is no place like home. (OMG!)

5) If it be necessary to determine the time, (second part of the sentence...)

Sorry for too many examples, but every time when I see "be', I'm stuck =) Why we cannot use is, are etc?
Are all sentences correct?

I'm trying to find the correct grammar rules but I have not been able to do it so far)

cheers, Sergey
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1 and 2 are examples of present subjunctive, used more in those days than nowadays
3 - 'Be' cannot be used there; it is a Conditional I, which uses indicative verb forms.
4 - as 1 and 2, or perhaps just a frozen poetic form: 'Home, Sweet Home' was written in 1822.
5 - as 1 and 2, an older form; we'd use 'is' now.
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Thank very much!