I can't help but notice that 'dziadek' takes the neuter ending in the Instrumental case. I'm assuming that the word is masculine. Does it take the neuter ending because of the ending part of the word, '-dek'? Or is it something entirely different?
"em" or "iem" are the endings for both masc. and neut. Instr.
you use "em" except when the stem ends in a velar (g or k), when you use "iem". There's a spelling rule in Polish that you should try and avoid "e" after velars...
"The letter e is usually separated from a preceding k or g by i,"
Swan, Oscar (2008-10-12). Polish Verbs & Essentials of Grammar, Second Edition (Verbs and Essentials of Grammar Series) (Kindle Location 201). McGraw-Hill Education. Kindle Edition.
The notes about the instrumental case back in those exercise were a bit sketchy a while back but they've tightened them up a bit since...
Człowiek takes the neuter ending also and it's masculine, maybe they are exceptions?
According to this wikipedia article, it is an irregular noun (scroll down passed 'Neuter Nouns'), but possibly only in the plural sense. As far as I can tell, it doesn't explicitly tell what gender the word is, or how it declines. I think it may be because of hard/soft sounds, but I am not entirely sure. Article: https://en.m.wikipedia.org/wiki/Polish_morphology#Nouns
I read somewhere in the comments that the words ending in 'k' or 'g' take 'iem' in the instrumental. It is because of 'e' in 'dek' but I don't know why exactly :)
It is not because of the 'e' in '-dek' but because of 'k' and 'g'. If they are the last consonants of a word then they are never followed by a single 'e' or 'y'. If the suffix normally begins with 'e' it becomes 'ie' and if it normally begins with 'y' it becomes 'i'.