Does this equal that

They'll be down anytime now. = They should be here anytime now

I knew they were going to come down any time now. (can you use "any time now" with the past?) [umm, nope, "... at any time."]

I meant this definition: If you say that something will happen any day now, any moment now, or any time now, you mean that it will happen very soon.
♦ any day/moment/time now phrase PHR with cl
Jim expects to be sent to Europe any day now..., Any moment now the silence will be broken.
so what do you think: Not possible in the past tense?
I knew they were going to come down any time now.

Does "at any time" mean "any time now" or what does it mean
Not possible in the past, but you could try 'any time then': that might work.

Any time now = very soon.

At any time = at an indefinite time.
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So you coud say it like

She is going to call any time now.

She should be down any time now.

She will be down any time now.

Can you use any time now with will and should?
Those are all fine. There is no relationship between the phrase and the modal verbs.