Learn Portuguese (Portugal): A loja tem tido sucesso.

In Portuguese, this grammar structure (the present tense of ter plus a past participle like tido) is used for actions that started in the past and are still happening repeatedly or continuously. So tem tido doesn't mean it happened just once; it means the shop has been continuously having success right up to the present.

Where is the verb for 'doing' in the Portuguese sentence?

The English translation 'doing well' is just a natural way to express the Portuguese phrase ter sucesso, which literally translates to 'to have success'. Languages often use different verbs for the same concept, so Portuguese uses ter (to have) where English uses 'to do' or 'to be'.

Could I use the simple past and say A loja teve sucesso instead?

You could, but it changes the meaning. The simple past teve implies that the shop was successful at a specific time in the past or that the success has ended. By using tem tido, you emphasize that the success is an ongoing trend that is still happening today.

Why is there no article before sucesso?

In Portuguese, abstract nouns like sucesso (success), sorte (luck), or paciência (patience) generally do not need an article when they follow the verb ter. You simply use ter sucesso without any word for 'a' or 'some' in between.