1
For an example,

Mi ne scias kiel mi diras.
(I don't know how I have to say)

Can I restate this sentence as

→ Mi ne scias kiel diri.
(I don't know how to say)

Does it make sense in Esperanto?

2
Can I omit interrogatives when I have to use it again after 'ke ~'.

For an example,

Ĉu vi sciigu al mi ke, kiel mi povas malfermi kiu pordon?

→ Ĉu vi sciigu al mi kiel mi povas malfermi kiu pordon?

3
Ŝi kalkulas pli rapide ol ni kalkulas per maŝinoj.
(She calculate faster than we do with machines)

'kalkulas' appears twice in this sentence. Can I replace it to something else to shorten it? (such as 'do', 'did' in English)

* fari? maybe?

Bonvolu helpi min! Mi amas vin ĉiujn.

apriliss:1
For an example,

Mi ne scias kiel mi diras.
(I don't know how I have to say)

Can I restate this sentence as

→ Mi ne scias kiel diri.
(I don't know how to say)

Yes, you can say that, your second sentence is fine. Your first sentence is a little strange even, I'd say it as "Mi ne scias kiel mi devus diri" or "Mi ne scias kiel mi devas diri"

2
Can I omit interrogatives when I have to use it again after 'ke ~'.

For an example,

Ĉu vi sciigu al mi ke, kiel mi povas malfermi kiu pordon?

→ Ĉu vi sciigu al mi kiel mi povas malfermi kiu pordon?

Your sentences both don't make a lot of sense but it's not from the removal of a word. Your sentence seems to read "Should you let me know how I can open which door?"

I wonder if you meant to have it read "Would you let me know how I can open that door?". I'm going to assume that's what you meant, just so that we're starting out from a starting point of a sentence that I definitely know the intended meaning of.

That sentence would read "Ĉu vi sciigus al mi kiel mi povas malfermi tiun pordon?" or else, another correct alternative would be "Ĉu vi sciigus al mi kiel malfermi tiun pordon?"

"ke kiel" is a combination I would never expect to see.

3
Ŝi kalkulas pli rapide ol ni kalkulas per maŝinoj.
(She calculate faster than we do with machines)

'kalkulas' appears twice in this sentence. Can I replace it to something else to shorten it? (such as 'do', 'did' in English)

There is no Esperanto equivalent of "do" or "did" to avoid repeating a verb.

But you can leave out a verb entirely when it is understood through context.

I assume that the full meaning of the sentence is that she counts more quickly by hand (or by brain?) than we do with machines. That would be important in the shortened version. It could be, for example, "Ŝi kalkulas pli rapide permane [or "mense", maybe] ol ni per maŝinoj"

erinja:

apriliss:1
For an example,

Mi ne scias kiel mi diras.
(I don't know how I have to say)

Can I restate this sentence as

→ Mi ne scias kiel diri.
(I don't know how to say)

Yes, you can say that, your second sentence is fine. Your first sentence is a little strange even, I'd say it as "Mi ne scias kiel mi devus diri" or "Mi ne scias kiel mi devas diri"

2
Can I omit interrogatives when I have to use it again after 'ke ~'.

For an example,

Ĉu vi sciigu al mi ke, kiel mi povas malfermi kiu pordon?

→ Ĉu vi sciigu al mi kiel mi povas malfermi kiu pordon?

Your sentences both don't make a lot of sense but it's not from the removal of a word. Your sentence seems to read "Should you let me know how I can open which door?"

I wonder if you meant to have it read "Would you let me know how I can open that door?". I'm going to assume that's what you meant, just so that we're starting out from a starting point of a sentence that I definitely know the intended meaning of.

That sentence would read "Ĉu vi sciigus al mi kiel mi povas malfermi tiun pordon?" or else, another correct alternative would be "Ĉu vi sciigus al mi kiel malfermi tiun pordon?"

"ke kiel" is a combination I would never expect to see.

3
Ŝi kalkulas pli rapide ol ni kalkulas per maŝinoj.
(She calculate faster than we do with machines)

'kalkulas' appears twice in this sentence. Can I replace it to something else to shorten it? (such as 'do', 'did' in English)

There is no Esperanto equivalent of "do" or "did" to avoid repeating a verb.

But you can leave out a verb entirely when it is understood through context.

I assume that the full meaning of the sentence is that she counts more quickly by hand (or by brain?) than we do with machines. That would be important in the shortened version. It could be, for example, "Ŝi kalkulas pli rapide permane [or "mense", maybe] ol ni per maŝinoj"

Thanks so much!! I've learned a lot... God bless you