A very cool puzzle. 

>! Obviously the starting formulas are shown as a logic example: we can combine elements referenced by numbers to get other elements (numbers).
>! Also now we know for sure that fire+air does not result in stains :)

Encryption method:
>! 3+4, or electricity plus fire - since gravity is a hint for the key, could be Sun (or Star)
>! After seeing another hint, "electrical ties" could also mean nuclear bond (wut). McChiken or a burger with fries could hint to fat(46), meat(48), crisps(23) or fire(4).
>! UPD1: **Arcfour** = Arc(electricity)+four(fire). Its the encryption method.
>! UPD2: not sure if accidental, but CBC(Cypher block chaining) looks just like chicken bacon and crisps. 

Encryption key:
>! Gravity ( minus all?). 
>! After seeing the second hint, it only strengthens my suspicion of space bodies or processes involved here.
>! UPD2: key = **zero gravity**... (tried a hundred more complicated keys, meh)

Another hint:
>! Not sure what it means, but possibly: Pl - P = Plastic (or Playdoh) - Paint = 56(or 42) - 28 = 28 (or 14, which is papier mache)
>! UPD2: the encrypted message was also scrambled. Tested rot14, then noticed that P is also plague(19): 42-28= **rot23**, which unscrambled the message.

The last part:
>! "The puzzle contains the answers, look beyond the chart; Several numbers given, the words can surely tell" - ok, that seems to mean that we have to get words from paragraphs, starting from the paragraph right after the chart. Tried different paragraphs and ideas, but the only sensible result is "The professor's thesis (dive) (a)"... so there is something wrong with this approach. Also tried including the paragraph with formulas (4 + 20 = 61... etc), no luck so far.
>! An interesting part is "count the stars, this professor isn’t well". The third paragraph has "hydrogen or helium", and there are other hints to stars in the puzzle. The whole theme is space, after all.
>! Also, 11th word in the encrypted message is "technology".