Bayan aiki, ina tafiya a titi a hankali.

Yes. Bayan aiki means after work and it works as an introductory time phrase.

• bayan = after (also can mean behind, depending on context)
• aiki = work
  It’s a common structure: bayan + noun = after + noun.

In Hausa writing, punctuation is flexible, but the comma is fine and often used when a time phrase comes first. You can write:

• Bayan aiki, ina tafiya a titi a hankali. (very natural)
• Bayan aiki ina tafiya a titi a hankali. (also acceptable)

Both can be correct depending on the structure.

• Bayan aiki is common and means after work in a general sense.
• Bayan aikin often appears when aikin is followed by something that completes it, like possession or a specific phrase, e.g. bayan aikin yau = after today’s work.
  In many everyday sentences, bayan aiki is perfectly idiomatic.

Yes—ina? can mean where? as a question. But in statements, ina + verb is a common progressive/ongoing form meaning I am (verb)-ing.
So here:

• ina tafiya = I am walking / I am going

Context and intonation help distinguish them:

• Question: Ina? (Where?)
• Statement: Ina tafiya... (I’m walking...)

They express different aspect/tense:

• ina tafiya = I am walking / I usually walk (ongoing or habitual, depending on context)
• na tafi = I went / I have gone (completed action)

So this sentence paints a scene: after work, you’re in the process of walking along the road slowly.

In Hausa, a is a very common preposition that covers several English ideas like in/on/at/by/with depending on the phrase.

• a titi = on/in the street, along the road
• a hankali = slowly (literally something like in calmness/care)

So using a multiple times in one sentence is normal.

titi can mean street/road in general. a titi usually just means along the street/road (i.e., outdoors on the roadway area), not necessarily literally in the middle of traffic. If you want to be more specific, Hausa can add details, but a titi is the normal default.

Yes, a hankali functions like an adverb meaning slowly / carefully / gently. It commonly comes:

• at the end of the clause (as here): ...a hankali
• or right after the verb in some contexts

Placing it at the end is very natural and emphasizes the manner.

Not in a normal full sentence. Hausa typically needs a subject/tense marker like ina (I am...), kana (you are...), yana (he is...), etc., or a completed-action marker like na.
So you’d normally keep:

• ina tafiya... (I’m walking...) or use another correct form:
• na yi tafiya... (I did a walk / I walked—more formal/less common for this exact meaning)

A learner-friendly guide:

• Bayan: roughly BA-yan (two syllables)
• aiki: AI-ki (the ai is like the vowel in English eye)
• ina: EE-na
• tafiya: ta-FEE-ya (the middle syllable is stressed by many learners, but keep it smooth)
• titi: TEE-tee
• a hankali: a han-KA-lee
  Hausa is fairly consistent: vowels are usually clearly pronounced, and syllables are evenly timed.

Yes, it can, depending on context. ina + verb can describe:

• something happening right now (ongoing): after work (today), I’m walking slowly
• a usual routine (habitual): after work, I walk slowly

If you need to force the habitual meaning, speakers may add context words like kullum (every day) or yawanci (usually).