Learn Arabic (Modern Standard): عفوا، لا مشكلة.

This is the visible indefinite accusative case! The base noun is عفو (pardon or forgiveness). Many fixed expressions, greetings, and adverbs use this grammatical case, which adds an Alif and an "-an" sound to the end, making it عفوا (afwan).

I don't see the double vowel marks (tanween) over the Alif in عفوا. How do I know how to pronounce it?

In everyday Arabic writing, the two little lines indicating the "-an" sound are often left out. However, because the extra accusative Alif is visible at the end of the word, it acts as a big clue. You will always pronounce this word as "afwan", never "afwaa".

If the word مشكلة (problem) were in the accusative case, would it also get an extra Alif?

No. Words that end with the feminine marker taa marbuta (ة) never take an extra Alif, even when they take the "-an" accusative sound. If you needed to write it with that case, you would just write the double vowel marks directly over the letter, like مشكلةً.

We previously learned that ليس means "is not". Why do we use لا to say "no problem"?

You use ليس when negating a specific state, like saying "the book is not big". You use لا directly before a noun to express that a category of things doesn't exist at all. So لا مشكلة literally means "there is absolutely no problem".