Mi ne havas tiom da tempo kiom vi, do mi devas rapidi.

Tiom ... kiom is a comparison pattern for quantity. It means as much ... as.

So:

Mi ne havas tiom da tempo kiom vi
= I do not have as much time as you

Because the sentence is negative, the overall meaning becomes not as much ... as.

A useful comparison:

• tiom ... kiom = comparison of amount/quantity
• tiel ... kiel = comparison of degree/quality/manner

For example:

• Mi havas tiom da mono kiom vi. = I have as much money as you.
• Mi estas tiel laca kiel vi. = I am as tired as you.

Da is used after words that express quantity or amount.

So:

• tiom da tempo = that much time / so much time
• literally, something like that amount of time

This is very common in Esperanto after quantity words such as:

• multe da = a lot of
• iom da = some
• tiom da = that much / so much
• kiom da = how much / how many

Examples:

• Mi havas multe da laboro. = I have a lot of work.
• Ŝi trinkis iom da akvo. = She drank some water.

So in your sentence, tiom da tempo is the natural way to say so much time / as much time.

Because tempo here is being treated as an uncountable noun, just like time in English.

We normally do not count times here as separate units; we mean an amount of time in general. So:

• tiom da tempo = as much time

Using tempoj would suggest separate, countable instances or periods, which is not the meaning here.

Compare:

• Mi ne havas multe da tempo. = I do not have much time.
• La tempoj ŝanĝiĝas. = Times are changing.

In your sentence, singular tempo is exactly what you want.

Because Esperanto often leaves out repeated words when they are obvious from context.

The full version would be:

Mi ne havas tiom da tempo kiom vi havas.

But since havas is already understood, it is natural to shorten it to:

Mi ne havas tiom da tempo kiom vi.

English does this too:

• I don’t have as much time as you (do).

The verb is understood, so it does not need to be repeated.

By itself, kiom often means how much or how many, but in this structure it is part of the comparison tiom ... kiom.

So here kiom vi does not mean a direct question like how much you?
Instead, it means something like:

• as you do
• as much as you have

So the meaning comes from the whole pattern, not from translating each word separately.

In Esperanto, ne usually goes directly before the part it negates. Here it negates the verb:

• Mi ne havas = I do not have

This is simpler than English because Esperanto does not need do-support. English says:

• I do not have

but Esperanto just says:

• Mi ne havas

So ne before havas is the normal way to make the sentence negative.

Do means so, therefore, or thus.

It shows that the second part of the sentence is the result or consequence of the first:

• Mi ne havas tiom da tempo kiom vi, do mi devas rapidi.
• I don’t have as much time as you, so I have to hurry.

It is a very common connector in Esperanto.

A few similar ideas:

• ĉar = because
• do = so / therefore

Compare:

• Mi rapidas, ĉar mi ne havas multe da tempo. = I am hurrying because I do not have much time.
• Mi ne havas multe da tempo, do mi rapidas. = I do not have much time, so I am hurrying.

After devas and other modal verbs, Esperanto uses the infinitive.

So:

• devas rapidi = must hurry / have to hurry

Not:

• devas rapidas ❌

This is similar to English:

• I must hurry
• not I must hurries

Common modal-style combinations in Esperanto:

• mi povas iri = I can go
• ŝi volas manĝi = she wants to eat
• ni devas labori = we must work

So mi devas rapidi is exactly correct.

Because rapidi is the verb meaning to hurry or to be in a hurry.

Related forms are:

• rapida = fast, quick
• rapide = quickly
• rapidi = to hurry

So:

• Mi devas rapidi. = I have to hurry.
• Li estas rapida. = He is fast.
• Ŝi parolas rapide. = She speaks quickly.

A native English speaker may expect something more like be quick, but Esperanto often uses a simple verb here: rapidi.

Yes. You can say:

Mi ne havas tiom da tempo kiom vi havas, do mi devas rapidi.

That is completely correct and maybe a little more explicit.

But the shorter version:

Mi ne havas tiom da tempo kiom vi, do mi devas rapidi.

is also completely natural, because the missing havas is easy to understand.

So both are grammatical; the version without the repeated verb is simply more concise.