Learn Hardcore Turkish: Yalnız kalınca daha iyi odaklanabiliyorum.

It’s a temporal adverbial suffix meaning “when/once/whenever.”
It attaches to a verb stem: kal- (stay/remain) + -ınca → kalınca.
It carries no tense or person; the main clause sets tense/person.
It follows vowel harmony and appears as -ınca / -ince / -unca / -ünce (a/ı → ınca; e/i → ince; o/u → unca; ö/ü → ünce).

Could I say yalnızken or yalnız olduğumda/yalnız kaldığımda instead of yalnız kalınca? What are the nuances?

yalnız kalınca: literally “when (I) end up/stay alone.” Slight change-of-state feel, but often just means “when (I am) alone.”
yalnızken: “while (I am) alone,” focusing on the state; short and very common.
yalnız olduğumda: “when I am alone,” explicit 1st person via -DIK + possessive + -DA; a bit more formal/precise.
yalnız kaldığımda: nominalized version of “when I am/was left alone,” similar in meaning to kalınca. All are idiomatic; pick based on nuance or formality.

What about yalnız olunca? Does that work?

Yes. yalnız olunca is also common and neutral: “when (I) am/become alone.” Compared to kalınca (“remain/left alone”), olunca avoids the “left/remain” nuance.

Why use odaklanabiliyorum with -yor? For a general statement, shouldn’t it be odaklanırım or odaklanabilirim?

odaklanırım: aorist; sounds habitual/gnomic (“I (do) focus” as a general truth).
odaklanabilirim: aorist with ability; “I can focus (in principle).”
odaklanabiliyorum: present progressive with ability; very common in speech for current tendency and even for general claims. With -ınca clauses, aorist is more textbook-habitual, while -yor is more conversational; both are fine.

What exactly is inside odaklanabiliyorum?

odak + lan + a + bil +iyor + um

odak: focus (noun)
-lan: inchoative/reflexive (“to become focused / to focus oneself”)
-a-: thematic vowel
-bil-: ability/possibility (“can”); it surfaces as -abil- here because the preceding vowel is back (a)
-iyor-: present continuous
-um: 1st person singular Altogether: “I am able to focus.”

Could I just say odaklanıyorum instead of odaklanabiliyorum?

Yes, but the nuance shifts:

odaklanıyorum: the action (“I (am) focus(ing)”).
odaklanabiliyorum: the ability/possibility (“I can/am able to focus”). In conditional statements (“when X, I can Y”), the -abil- form is especially natural.

Where does daha iyi go in the sentence? Can it come after the verb?

Place degree adverbs before the verb phrase: yalnız kalınca daha iyi odaklanabiliyorum. Putting it after the verb (… odaklanabiliyorum daha iyi) is unusual unless you want marked, speech-like emphasis. You can front it for emphasis: Daha iyi odaklanabiliyorum, yalnız kalınca.

How do comparatives work here? Why not use a suffix for “better”?

Turkish uses daha (“more”) with adjectives/adverbs:

iyi → daha iyi (good → better) For the superlative, use en: en iyi (best). You can intensify with çok daha (“much better”). Don’t say “daha fazla iyi.”

Why odaklanmak and not odaklamak?

odaklanmak: intransitive/reflexive, “to focus (oneself/one’s attention).” It typically uses the postposition: bir şeye odaklanmak (“to focus on something”).
odaklamak: transitive, “to focus (something),” e.g., kamerayı odaklamak (“to focus the camera”) or dikkatini bir şeye odaklamak (“to focus someone’s attention on something”). Your sentence is about self-focusing, so odaklanmak is the natural choice.

Who is the subject of kalınca? How do I know it’s “I”?

-ınca clauses don’t show person. The subject is inferred from context or stated overtly.
Here, with no overt subject in the subordinate clause and a 1sg main verb (-um), it’s understood as “when I …”.
You can specify a different subject: Ali yalnız kalınca gidiyorum (“When Ali is alone, I leave”). Compare: Ali gelince gidiyorum (“When Ali comes, I leave”).

Does yalnız ever mean “only” or “however”? How can I tell what it means here?

Yes:

As adjective/adverb: yalnız = alone; also “only/merely” (synonym of sadece) when it precedes what it limits: Yalnız bir saatim var (“I only have an hour”).
As a sentence adverb: Yalnız, … = “However, …” In yalnız kalınca, it directly modifies the state with a verb, so it means “alone.”

Pronunciation tips: How do I say yalnız kalınca and odaklanabiliyorum?

ı is the dotless i, a close central unrounded vowel (a short, relaxed “uh” with no lip rounding).
c is like English “j” in “jam.” So kalınca ≈ [ka-lɯn-dʒa].
odaklanabiliyorum: each syllable is pronounced; -yor is [joɾ]. In fast/informal speech, final -r may soften/drop: odaklanabiliyom.

Should there be a comma after kalınca?

Often yes in formal writing: Yalnız kalınca, daha iyi odaklanabiliyorum. It’s an initial adverbial clause. In informal writing, many omit the comma; both are acceptable.

How do I make negative and question forms of the main clause?

Negative (can’t): Yalnız kalınca daha iyi odaklanamıyorum. (odaklan-a-ma-ıyor-um → odaklanamıyorum)
Yes/no question: Yalnız kalınca daha iyi odaklanabiliyor musun?/musunuz?
Negative question: Yalnız kalınca daha iyi odaklanamıyor musun? Note: “daha iyi odaklanamıyorum” literally means “I can’t focus better,” which is odd; use iyi odaklanamıyorum if you mean “I can’t focus well.”