Сейчас я закончу работу, а потом позвоню бабушке.

In Russian, Сейчас can mean right now / at this moment, but it often introduces an action that is about to happen and will be completed soon. With that “immediate future” meaning, Russian typically uses the future of a perfective verb: Сейчас я закончу… = I’ll finish (in a moment) rather than I am finishing.

Both are future tense forms, but specifically the simple future of perfective verbs:

• (я) закончу = I will finish (and it will be completed)
• (я) позвоню = I will call (make a call as a completed action)

Perfective verbs don’t have a true present tense meaning; their “present” forms refer to the future.

The given sentence uses perfective because it describes two completed, one-time actions in sequence: 1) finish the work, 2) call grandma.

If you say Сейчас я заканчиваю работу, that uses imperfective and focuses on the process: I’m in the middle of finishing up.
But а потом звоню sounds odd without a broader context; for a planned next step you’d usually still use future: а потом позвоню. A more natural process-focused version could be:

• Сейчас я заканчиваю работу, а потом позвоню бабушке.

• сейчас = right now / in a moment (immediate timeframe)
• теперь = now in the sense of from now on / at this stage (contrast with earlier)
• сегодня = today (the day as a whole)

Here Сейчас fits because it’s about finishing soon, then doing the next action.

Because this is a compound sentence with two clauses:

• Сейчас я закончу работу,
• а потом (я) позвоню бабушке.

Russian normally uses a comma between such clauses, especially with connectors like а.

а often means and / but, but it usually adds a sense of shift or contrast between parts. Here it’s like and then / and after that with a mild “next step” transition.

и потом is also possible and more purely additive (and then), but а потом is very common in conversational sequencing.

Because работа is the direct object of закончить (to finish). For an inanimate feminine noun:

• nominative: работа
• accusative: работу

So закончу (что?) работу.

Because позвонить takes the person you call in the dative:

• позвонить (кому?) бабушке = to call (to) grandma

The called person is treated like an indirect recipient of the call.

No—standard Russian does not use позвонить + accusative person. It’s позвонить + dative: позвоню бабушке.

If you want an accusative direct object, you’d use a different verb: вызвать (to summon/call for) or in some contexts набрать (to dial a number), but for “call someone (by phone)” the normal verb is позвонить кому-то.

Russian often omits repeated subjects when it’s obvious. After я закончу, it’s clear the second action has the same subject, so (я) is dropped:

• …а потом позвоню бабушке.

You can include я for emphasis or clarity:

• …а потом я позвоню бабушке (slightly more emphatic).

The given order is very natural. потом is flexible:

• …а потом позвоню бабушке (common)
• …а позвоню потом бабушке (emphasizes that the call happens later)
• …а потом бабушке позвоню (puts focus on grandma, often contrastive)

Moving words changes emphasis more than core meaning.

Stress matters a lot in Russian:

• позвоню́ (stress on the last syllable -ню́)
• закончу́ (stress on the last syllable -чу́)

Approximate guide:

• паз-ва-NYOO (with a clear stressed ending)
• за-KON-choo (ending stressed)