Just as a side note, some adult cats are lactose intolerant and shouldn't be given milk. Kittens should not be fed cow milk as well, if there are alternatives. IIRC goat milk is better, but adapted milk for kittens would be even better (if the kittens can't drink their mom's milk, of course).
"-le" is the suffix form of of "ile (with)". -lık/lik" is a suffix which makes nouns from nouns (güzel+lik, çocuk+luk, kesin+lik etc.). So the correct deconstruction is like that: genel+lik+le. I do not know how to say it literally. Maybe"With generalization" and "with certainity" for "kesinlikle"?
in turkish, in terms of verbs, there are two kind of sentences. they are called ''isim cümleleri=noun sentences'' and ''fiil cümleleri-(action)verb sentences''
Kediler süt içer = cats drink milk : this sentence is a ''fiil cümlesi'' because 'drink' is a ''fiil''
kediler hayvandır = cats are animals : in this sentence, the verb is 'hayvan-dır' and hayvan=animal is a noun.
-dir is used in ''noun sentences=isim cümleleri''
to sum up, if the verb is ''to be'' then you can use -dir.