Yes, this particular “double-would” scenario is perfectly fine (unlike most of them).
That’s because the first would in your sentence is the one that means to be willing or wanting to do something. It’s about willingness, volition.
Read it this way:
If only the Israelis had ever once been willing to just say that we got screwed in 1948 and that they're sorry it happened, we would be willing to make peace.
The reason speakers of foreign languages are told they should “never” use will or would in the if part of a conditional is not because this is true, but because it stops them from making common blunders that native speakers simply do not say.
For example, these are all wrong but are commonly heard from learners trying to compose valid English conditional constructions:
- If it *will rain, we will stay home.
- It if *would rain, we would stay home.
- If it *would have rained, we would have stayed home.
It is easy to correct those to make them grammatical:
- If it rains, we will stay home.
- It if rained, we would stay home.
- If it had rained, we would have stayed home.
However, your example sentence did not use would in the if part incorrectly. That’s because this is the version of that verb which means to want to or to be willing to. It is about willingness, not about probability. Given that only animate subjects can be willing, it is impossible to use this form in the if it rains examples given above.
However, it is perfectly normal to use if you will or if you would in de-facto requests like these:
- If you will please give me your name, we can get started here.
- If you would please give me your name, we can get started here.
As you see, these are more like polite requests than they are expressions of a non-real scenario in the if part. The reason would happens in the second version is because we routinely backshift to make a request more polite. Therefore the second of these is more polite than the first:
- Will you please give me your name so we can get started here?
- Would you please give me your name so we can get started here?
There are other, rarer occasions to use would in conjunction with if. One of those is when it’s an if only:
- If only it would rain!
- If only it were so!
Those two are cases for which some languages use an dedicated optative mood to express, but English doesn’t have that. But English does use the same forms with wish that it uses with if only:
- I wish it would rain.
- I wish it were so.
This is not intended to be an exclusive set of all possible legal if + will/would combinations that natives use but learners are seldom taught. There are more possibilities that are legal. Native speakers create far more forms of conditionals, all grammatical, than learners are ever taught.
The directive “never” to use will or would in a conditional is a simplified version of reality that attempts to block common errors. No native speaker is ever told this.
For your other question, to be/get screwed means to be cheated or to be unfairly made to suffer some loss or figurative injury at someone else's hand, and there's nothing that can be done about it.