Confusion over when definite article use is necessary

Question

I just completed a translation exercise which included the following sentence:

"... we see the fireworks and we receive gifts from Father Christmas."

I translated the sentence as follows: "... vemos los fuegos artificiales y recibimos regalos desde Papá Noel". Kwiziq indicated that the correct translation should have been "... vemos los fuegos artificiales y recibimos los regalos de Papá noel."

I have two question about this:

1) Why was it necessary to insert "los" in front of "regalos"? I do not understand fully the rule of when the definite articles (singular or plural) must be used. As you can see, I inserted it when "the" was included before "fireworks" in the English translation, but omitted "los" when "the" was not included before "gifts" in the English translation. Again, what's the rule on this? When I practice the writing exercises seems use of articles is hit and miss.

2) I am confused about why "de" was used as translation of "from" instead of "desde". Seems "regalos de Papá Noel" would translate in English to Santa Claus's gifts. Please explain.

Thank you!

Pati Ecuamiga.

Accepted Answer

Hola Pati
With regards to your first question about the inclusion or not of the second article, you can use it or omit it. We'll make sure this is reflected in the exercise so both options are fine. 
The definite article is one of the most difficult topics to master when learning Spanish because there isn't any clear cut rule for when to use them or when to omit them, other than in specific scenarios which we have in lessons. For example, these ones:
Using the definite article with days of the week for events
Presence of the Spanish definite articles el/la/los/las
Using the Spanish definite article or not with titles
In general, the use of the definite article is determined by how precise we are on the thing we are talking about. We tend to drop it when we refer to the noun in question in a more "generic" way. This is why most of the time it is very subjective. 
We'll try to expand on this topic so there is more useful information about it.
Af for your second question about "desde", desde does mean "from", but when something comes "from a person", we use "de" - It is when talking about "from somewhere" that we can use either "desde" (and sometimes "de"). For example:
No he recibido ningún correo de ese cliente.
I haven't received any e-mail from that client. 
¿Has caminado desde tu casa? 
Have you walked from home?
I hope this clarified it.
Saludos