Learn Hardcore Turkish: Yedek plan devreye girer girmez sunuma kaldığımız yerden devam ettik. - As soon as the backup plan kicked in, we continued the presentation where we left off.

It means as soon as. It’s a fixed temporal construction built by repeating the same verb: affirmative aorist third-person singular + negative aorist third-person singular. Pattern: V-ar/er V-maz/mez (with vowel harmony).

girer girmez (from girmek)
gelir gelmez (as soon as he/she comes)
başlar başlamaz (as soon as it starts)
biter bitmez (as soon as it ends)
çıkar çıkmaz, olur olmaz, etc.

Why is it girer and not girdi in girer girmez?

Because this construction specifically uses the aorist (simple present) form, not the past. The pair aorist affirmative + aorist negative together creates the meaning as soon as, regardless of the actual tense of the main clause.

Can I use girince or girdikten sonra instead of girer girmez?

girince means when/once it enters; it doesn’t itself guarantee immediacy.
girdikten sonra means after it entered; it can suggest some delay.
girer girmez specifically conveys no sooner than / immediately after. If you want the strong immediate feel, keep girer girmez. If timing is looser, girince or girdikten sonra work.

What exactly does devreye girmek mean?

Literally into the circuit to enter. Idiomatically it means to be activated, to kick in, to be put into operation. It’s used for systems, policies, backup plans, safety mechanisms, generators, etc. The opposite idea is often devre dışı kalmak (to be out of service). A close synonym is faaliyete geçmek (to become operational).

Why is it sunuma and not sunumu?

Because devam etmek selects the dative case: you continue to/with something, so X‑e/a devam etmek. Hence sunuma devam ettik. If you want a transitive verb that takes the accusative, use sürdürmek or devam ettirmek: sunumu sürdürdük or sunumu devam ettirdik. Note that sunuma cannot mean my presentation; that would be sunumuma.

How does kaldığımız yerden work morphologically?

kal-: stay/remain (here: be left, stop)
-DIK: participle/nominalizer forming a relative clause
-ImIz: our (1st-person plural possessive)
The k of -dık softens to ğ before a vowel-initial suffix: kaldığımız
yer: place; -den: from So kaldığımız yerden = from the place/point where we left off.

Does kalmak really mean to stay? How does it mean leave off here?

Yes, kalmak primarily means to stay/remain, but in the set phrase kaldığı yer it idiomatically means the point where one had stopped. You’ll also hear bıraktığı yer with the same meaning. In practice, kaldığımız yerden and bıraktığımız yerden are both common and near‑synonymous in this context.

Why do we have devam ettik and not simply a single verb?

Devam etmek is a light-verb construction (noun + etmek) meaning to continue. In the past tense it becomes devam ettik (note the assimilation: et-di → etti → ettik). You could also use a simple verb like sürdürmek (to sustain/continue something) when you want a direct object: sunumu sürdürdük.

Do I need a comma after Yedek plan devreye girer girmez?

It’s optional but recommended for readability, since the initial clause is an adverbial time clause. Both are seen:

Yedek plan devreye girer girmez, sunuma...
Yedek plan devreye girer girmez sunuma...

Is sunuma necessary, or can I drop it?

You can drop it if the context already makes the topic clear: Kaldığımız yerden devam ettik still means we continued from where we left off. Keeping sunuma explicitly states that what resumed was the presentation.

Can the subjects be different in the two parts? Here it’s the plan vs. we.

Yes. The V‑er V‑mez time clause is non-finite and doesn’t force the same subject as the main clause. Your sentence is perfectly normal: the plan kicked in, and then we continued.

How would I change kaldığımız for different persons?

I: kaldığım yerden
You (sg): kaldığın yerden
He/She: kaldığı yerden
We: kaldığımız yerden
You (pl/formal): kaldığınız yerden
They: kaldıkları yerden

Could I say devam etmeye başladık instead of devam ettik?

You can, but it adds a nuance: devam etmeye başladık emphasizes the onset of resuming (we started to continue), which can sound a bit redundant. Devam ettik is the default, concise way to say we resumed/continued.

Is the word order fixed, or can I move things around?

Turkish is flexible as long as the finite verb stays at the end. These are all fine:

Yedek plan devreye girer girmez, sunuma kaldığımız yerden devam ettik.
Yedek plan devreye girer girmez, kaldığımız yerden sunuma devam ettik.
Kaldığımız yerden sunuma, yedek plan devreye girer girmez devam ettik. Fronting kaldığımız yerden for emphasis is also common.

Any synonyms or near-synonyms for yedek plan and devreye girmek?

yedek plan: B planı, alternatif plan, yedek çözüm
devreye girmek: faaliyete geçmek, hizmete girmek, aktif hâle gelmek (context-dependent)