Couple of questions for you --
You say that you're "starting to learn Greek" -- what does this mean exactly? Are you working through a textbook? How far have you gotten? I ask this because it makes a difference in how I answer you and what knowledge I can assume you already have and what you don't.
Second question: what dictionaries are you using?
I own the Intermediate Liddell Scott Greek-English Lexicon, this is pretty standard and what most students of classical Greek are told to purchase. It's adequate for most needs unless you're reading authors with a love of obscure vocabulary.
Looking up words can take a bit of practice, as it's not always simple to identify the headword that you should be looking under.
Looking at my dictionary, it includes an entry for βασκανος: "slanderous, envious, malignant"
πολυμεριμνος is not in my dictionary, but under μεριμνα I find: "care, thought, expecially anxious thought"
πολυ- is a common prefix, particularly in Homer, used for epithets. It means "many" or "full of"
There's nothing to do with "νους" here.
It is quite common to find -ν- added to a noun stem to form an adjective.
-ους is the accusative plural ending for o declension nouns and adjectives
For future searches, there's also a useful tool at the Perseus Digital Library: Dictionary Entry Lookup
If this isn't bookmarked, it should be.
The standard ancient Greek dictionary is Liddell, Scott, and Jones, usually abbreviated as LSJ. You can access it online (as well as the intermediate version, which is considerably shorter) at Perseus using spiphany's link, and you can also download Diogenes for offline access.
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