Learn French: Il y a un accident, alors je suis bloqué. - There is an accident, so I am stuck.

You can, but you have to flip the sentence around! Parce que introduces the reason: Je suis bloqué parce qu'il y a un accident (I am stuck because there is an accident). Alors introduces the result: Il y a un accident, alors je suis bloqué (There is an accident, so I am stuck).

Does alors always mean "so"?

In this context, yes! It means "so" or "therefore" to show the result of a situation. You will hear French speakers use alors all the time to connect their ideas.

If a female speaker is saying this sentence, does the word bloqué change?

Yes! Because bloqué describes the subject (je), it needs to match the speaker's gender. A woman would add an extra -e and write je suis bloquée. The pronunciation stays exactly the same either way.

I remember il means "he" and a means "has". Why does il y a translate to "there is"?

Il y a is a very common fixed expression. Word-for-word it translates to "it there has", but together the phrase always means "there is" or "there are". You don't change the words even if you are talking about plural things!