When are "because", "since","for" and "as" interchangeable?
Here's my opinion of your alternatives.
"because" is your best choice for clear, correct, unambiguous communication, especially if you want to be understood easily by other non-native speakers.
"since" is acceptable, although it makes your statement ambiguous; the second meaning would be that statement A became true at the time that statement B became true. Example: "I study more often since I enrolled in class" conveys that when you enrolled in class, then you began studying more often. Rule of thumb: prefer "since" when your intent is to convey "from the time that".
"as" is somewhat acceptable, but in your particular statement structure "as" has more useful meanings of "abstractly analogous" or "synchronously". Example: "I like apples as you like oranges" conveys that my liking is similar to your liking, i.e. equivalently strong/weak/notable/etc. Example: "I make dinner as you set the table" conveys that we do these tasks at the same time in the same place. Rule of thumb: prefer "as" when your intent is to convey "sameness".
"for" can be acceptable, although I would never expect to hear it in normal conversation. It would come across as overly-academic, or possibly epic or religious. Example: "We eat well tonight, for tomorrow we go to war." Rule of thumb: prefer "for" when you want to be poetic and inspirational.
From Longman contemporary dictionary:
BECAUSE (conjunction)
Used when giving the reason for something:
I went home because I was tired. The streets were flooded because of all the rain.
SINCE/as (conjunction)
Used when giving the reason why someone decides to do something or decides that something is true:
We decided to go to the beach since it was a nice day. I thought Kevin was out as his car wasn’t there.
DUE to/owing to (preposition)
Used to give the reason why something has happened. Due to and owing to are more formal than because:
The delay was due to a problem with the ship’s engines. The parade had to be cancelled owing to bad weather.
THROUGH (preposition)
Because of something. Through is used especially when saying why someone succeeded or failed to do something:
They won the game, more through luck than skill. You failed that test through carelessness.
THANKS to (preposition)
Used when explaining that something good has happened because of someone’s efforts, or because something exists:
Thanks to modern medicine, the disease can now be cured.
out of (preposition)
Because of a particular feeling or quality: He started reading the book out of curiosity. I only asked out of politeness.