Could an argument with false Premises and a true Conclusion be logically valid?
Validity is assessed on form only. Whether the premises are actually true or actually false is irrelevant.
Donald Trump is a martian;
All martians are Presidents of the United States of America;
Therefore, Donald Trump is President of the United States of America.
Valid argument, false premises, true conclusion. QED.
Note 1 on logical validity
The truth of the conclusion is not derived from the truth of the premises since the premises are (presumably) false. And it is also clearly not derived from the falsehood of the premises.
The truth of the conclusion is derived from the form of the argument, and by assuming that the premises are true.
If you understand the argument, then you should be certain, once you assume the premises, that the conclusion is true.
There is nothing else to it.
Aristotle didn't provide any more details as to how we arrive at the certainty that the argument is valid. And, so far, nobody else did, even though many great thinkers since Aristotle pondered the issue.
Note 2 on logical validity
Many logicians accept as valid arguments which are not formally valid. For example:
Everyone is female.
So, any siblings are sisters.
This argument will be accepted on the semantic ground that, first, the definition of the word "sister" in English makes any sister female by definition and, second, the definition of the word "sibling" in English makes any sibling either male or female.
However, semantic is a murky issue and admitting validity on semantic grounds can only lead to endless debates about the meaning of the words used in the argument which are not logical terms (i.e. not "or", "imply", etc.).
Further, any definition accepted as relevant to justify validity on semantic ground, is de facto an assumption, i.e. an implicit premise.
Whenever an argument is admitted as valid on semantic ground, it should be possible to make it formally valid by making explicit all relevant definitions by incorporating them as additional premises of the argument.
Thus, the argument above could be made formally valid by making it "formal", as follows:
For all x, Brother(x) implies not Female(x);
For all y, Sibling(y) implies either Sister(y) or Brother(y);
For all z, Female(z);
Therefore, for any a, Sibling(a) implies Sister(a).
Here, we can ignore the semantic of the non-logical terms. The validity of the argument is now entirely a function of the form of the argument.
To qualify an informal argument as valid, without any qualification, is therefore seriously misleading. An informal argument is valid to you only because you admit, if only implicitly, all relevant definitions.
Try to get anyone who doesn't know the definition of the English words used in the argument to agree that the argument is valid! Good luck. And would you yourself sign a document written in any language you don't understand on being told that the document is valid?
All formally valid arguments are also informally valid. However, informally valid arguments are not necessarily formally valid.
Thus, it is never misleading to use the word "valid" to refer to formally valid arguments, but it is misleading to use it to refer to informal arguments. When talking about the validity of informal arguments, we should use the expression "informally valid".