Learn Turkish: Çiçekçiye havale yapacaktım ama vazgeçtim. - I was going to make a money transfer to the florist, but I gave up.

It combines the future tense suffix -acak with the past tense suffix -tı (plus the first-person ending -m). This "future in the past" structure is the standard way in Turkish to express intentions or plans that were interrupted or didn't happen, translating perfectly to "I was going to" in English.

Since we are learning the continuous action suffix -(y)adurmak, could we use yapaduracaktım instead?

You could grammatically, but it would sound very unnatural here. The suffix -(y)adurmak implies an action that continues without interruption (to keep on doing something). Because a money transfer (havale) is typically a single, momentary transaction rather than an ongoing continuous activity, the standard form yapacaktım makes much more sense for this specific task.

The verb vazgeçtim means "I gave up" or "I changed my mind." If we explicitly stated what we gave up on, how would the sentence change?

The verb vazgeçmek strongly pairs with the ablative case (-DAn). If you wanted to explicitly say "I gave up on making the transfer", you would turn the action into a verbal noun and add the ablative ending: havale yapmaktan vazgeçtim. In this sentence, the object is simply omitted because it is obvious from context.

Why does Çiçekçiye take the dative -e ending in this sentence?