بعد ساعة، كانت الطبخة جاهزة وطعمتها كتير منيحة.

Yes—here بعد ساعة means after an hour or an hour later.

• بعد = after
• ساعة = an hour

In natural English, you might translate it either way depending on context. Arabic commonly uses this structure to set the time frame before the main statement.

Because الطبخة is feminine.

In Arabic, the past form of كان changes for gender:

• كان = he/it was (masculine)
• كانت = she/it was (feminine)

Since الطبخة is a feminine noun, the sentence uses كانت.

Because adjectives have to agree with the noun they describe.

Here, جاهزة describes الطبخة, and الطبخة is feminine, so the adjective is feminine too:

• جاهز = ready (masculine)
• جاهزة = ready (feminine)

So كانت الطبخة جاهزة literally follows the pattern the dish was ready, with feminine agreement throughout.

In Levantine Arabic, الطبخة usually means the dish, the food that was cooked, or the meal/cooking depending on context.

In this sentence, it most naturally means the dish/the food.

A pronunciation note: in Levantine, الطبخة is often pronounced something like iṭ-ṭabkha or eṭ-ṭabkha, because the ل in ال assimilates before ط.

Here طعمتها means its taste or its flavor.

The -ها ending means her/its. Since الطبخة is a feminine noun, -ها refers back to it as its.

So:

• طعمة / طعمة = taste, flavor
• طعمتها = its taste / the taste of it

In this sentence, وطعمتها كتير منيحة means and its taste was very good.

Because Arabic words ending in ة often change when a suffix is added.

When the word stands alone, ة is usually pronounced like -a / -e. But before a pronoun suffix, it often shows up as -t-.

So:

• طعمة on its own
• طعمتها = its taste

This is a very common pattern. Another example:

• سيارة = car
• سيارتها = her car

كتير here means very.

So:

• كتير منيحة = very good

As for منيحة, it is feminine because it agrees with طعمة in طعمتها, and that noun is feminine.

Compare:

• منيح = good (masculine)
• منيحة = good (feminine)

So the phrase is feminine because the thing being described is the taste/flavor.

Because in Arabic, especially in everyday Levantine, speakers often leave out repeated words when the meaning is already clear.

So this:

• كانت الطبخة جاهزة وطعمتها كتير منيحة

is understood as something like:

• كانت الطبخة جاهزة وكانت طعمتها كتير منيحة

The second كانت is omitted because it is easy to understand from the first part of the sentence. This sounds natural in conversation and informal narration.