Después de revisar la batería, la mecánica consiguió arrancarlo.

Because de is a preposition, and in Spanish a verb that comes right after a preposition normally goes in the infinitive.

So:

• después de revisar = after checking
• not después de revisó

This is the same pattern as:

• antes de salir = before leaving
• sin comer = without eating
• al entrar = upon entering

If you want a fully conjugated verb after después, you usually need de que:

• Después de que revisó la batería, la mecánica consiguió arrancarlo.

That version is also possible, but después de + infinitive is very common and compact.

Yes. Here la mecánica means the female mechanic.

Spanish often uses the masculine and feminine forms for professions:

• el mecánico = the male mechanic
• la mecánica = the female mechanic

Be careful, though: la mecánica can also mean mechanics as a field, depending on context. In this sentence, it clearly means a person because of the action consiguió arrancarlo.

The comma separates the introductory time/action phrase from the main clause.

• Después de revisar la batería = introductory phrase
• la mecánica consiguió arrancarlo = main clause

In English, you would often write the same kind of comma:

• After checking the battery, the mechanic managed to start it.

In Spanish, this comma is very natural and helps readability.

It means to check the battery or to inspect the battery.

In this context, revisar is not usually as deep or technical as repair. It suggests examining it, testing it, or looking to see whether it is the problem.

So revisar la batería could involve things like:

• checking the charge
• checking the connections
• seeing whether the battery is faulty

That is true: arrancar has several meanings.

A very important one, especially with vehicles or engines, is:

• arrancar = to start an engine / get a vehicle started

So here:

• arrancarlo = to start it

In other contexts, arrancar can also mean things like:

• arrancar una página = to tear out a page
• arrancar una planta = to pull up a plant

The car-related meaning is extremely common in Spanish.

Conseguir + infinitive means to manage to do something or to succeed in doing something.

So:

• consiguió arrancarlo = she managed to start it

This suggests there was some difficulty or effort involved. It is a little stronger than simply saying:

• lo arrancó = she started it

With consiguió, the sentence implies that starting it was not easy, and she eventually succeeded.

Because Spanish allows object pronouns to attach to an infinitive.

So these are both correct:

• la mecánica consiguió arrancarlo
• la mecánica lo consiguió arrancar

Both mean the same thing.

This is common with infinitives, gerunds, and affirmative commands:

• quiero verlo / lo quiero ver
• está haciéndolo / lo está haciendo
• hazlo

In your sentence, attaching lo to arrancar is completely natural.

Lo does not refer to la batería here.

It refers to whatever was being started, most likely something masculine such as:

• el coche
• el motor
• el vehículo

That is why the pronoun is lo, not la.

This is a very common learner issue: the pronoun does not have to refer to the nearest noun. It refers to the thing being started.

So the idea is:

• she checked the battery
• then she managed to start it = the car/engine

Because it describes a completed action in the past.

• consiguió = she managed, she succeeded

The sentence presents the event as finished: she checked the battery, and then she successfully started it.

If you used the imperfect, conseguía, it would sound more like an ongoing, repeated, or background action, which does not fit this sentence as well.

So the preterite is the natural choice for a specific completed event.

Usually, yes.

In sentences like this, the normal interpretation is that the subject of the infinitive phrase is the same as the subject of the main verb. So the default reading is:

• After checking the battery, the mechanic managed to start it.

In other words, the mechanic checked the battery and then started it.

Spanish often leaves that understood instead of stating the subject twice.

Yes. That is also correct.

You have two common options:

• consiguió arrancarlo
• lo consiguió arrancar

Both are grammatical and natural. The difference is mostly one of style, rhythm, or emphasis.

Spanish often gives this flexibility with object pronouns when there is an infinitive.