No. 1: Yes, I think you have got it.
No. 2:
Im having trouble understanding your definitions as well...
'anything' and 'whatever' can be synonyms like this:
Give me anything (and I don't care what). Give me whatever (you can spare).
'No matter what (happens)' and 'no matter how' are synonyms of ANYWAY, or ANYHOW in the following sentence:
::I will do it anyway / I will do it, no matter what (happens).
But
"I will do it anything."

is wrong.
Also
"I will do anything"

and "I will do
it no matter what"

have very
different meanings.
and
"I will do no matter what"

is wrong.
::I don't think 'no matter what' is a good definition of 'anything.' :-p
However this is possible:
Anything you give me will be okay. / No matter what you give me, it will be okay.
Hope that that helps you. If you are still confused about the definitions in your dictionary, then please copy the whole definition word-for-word and letter-for-letter in your post, so that we can see the complete thing.
I suspect that you may need a better dictionary!!!