Learn Polish: Dobro wraca, wszakże każdy dobry czyn ma wartość. - Goodness returns; as is well known, every good deed has value.

Yes, you could perfectly well say Dobro wraca, wszak każdy dobry czyn ma wartość. Both words are used to introduce a statement the speaker considers an obvious truth. Wszakże is slightly more formal and emphatic, but in this specific context, they are virtually interchangeable.

I have seen wszakże used to mean 'however' or 'yet'. How do I know it means 'as is well known' in this sentence?

You have to rely on context. Wszakże is a tricky word because it can function as a synonym for jednak (however) or as an emphatic version of wszak (after all). Here, translating it as 'however' would not make logical sense. Because the second part of the sentence explains and supports the first part rather than contradicting it, it clearly means 'after all' or 'as is well known'.

Why does the word dobro end in -o here? Is it an adverb?

No, here dobro is a neuter noun meaning 'goodness' or 'the good'. While you already know dobrze as the adverb and dobry as the adjective, Polish often uses the -o ending to create abstract neuter nouns from adjectives. Another common example is zło (evil).

Why does the sentence use każdy dobry czyn instead of wszystkie dobre czyny?