"I do not see this dog."
Translation:Nie widzę tego psa.
"Pies" is a masculine animate noun. Such nouns have the same form in accusative and genitive.
Yes of course it is. Exceptions tend to go other way - tomatoes, bananas, text messages, tablets, facebook are animated.
Is there a sort of rule of thumb when it comes to identifying wether a word is Femanine or Masculine etc.?
Most words ending in a consonant are masculine, most words ending in -a are feminine, most words ending in -o are neuter.
As I mentioned in another comment, you confuse genders. 'tej' is feminine. 'pies' is masculine, so the right form is 'tego'.
Now I see you asked exactly the same question in March... ;)