Learn English – only if VS even if

First, let's talk about their interchangeability. There are some contexts where the two words could be used to mean "additional"; however, I think there seems to be a subtle difference in meaning when the word further is used:

The summit ended without any more talks.
The summit ended without any further talks.

I could not have run any further.
I could not have run any more.

In the case of the summit meeting, the word further hints that talks might have helped two sides come closer to an agreement. That's because one meaning of further is:

further (adv.) at or to a more advanced, successful, or desirable stage
_{(from NOAD)}

In the case of the tired runner, any further suggests a greater distance, while any more suggests a longer time. While those meanings overlap, I think further might be a better word for a runner dropping out of a marathon, while more might be a better word for someone working out on a treadmill. That's because further also means:

further (adv.) by a greater distance, or for a longer way
_{(from NOAD)}

As for the book, I think the best way to describe the latest edition of a book is:

a new edition of the book

You might use another when comparing two different editions of the same book:

I bought a new copy of A Study in Scarlet.
Really? I thought you already owned that book.
I do, but this was another edition.

It's harder to use further, because, in the context of publishing, I would interpret further to mean:

further (adj.) additional to what already exists or has already taken place or been done
_{(from NOAD)}

However, I suppose we could:

The publisher has indicated a reluctance to print any further editions of this book.

In that last sentence, the adjectives new or more could work in place of further.

Are you trying to use these in a specific context?

Provided that is the one that's more often used as a conjunction.It means that one thing happening is dependent on another thing happening.

I will come visit you provided that my car gets new tires.

Provided that this project succeeds, I will get a promotion.

Sometimes people drop the that and only use provided and it means the same thing.

Mark will come to the wedding provided Alice is not there.

Providing is usually a form of the verb to provide and means to supply/give.

He is providing the food.

I don't know if providing that is used a conjunction. Maybe some places? It's not in American English as far as I know.