Negoziamo una soluzione che rispetti la legge e questo diritto.

It can mean either, depending on context.

• Noi negoziamo = we negotiate
• Negoziamo! = let’s negotiate!

In this sentence, without an explicit subject, negoziamo is very naturally understood as an exhortation: let’s negotiate. Italian often uses the 1st person plural present tense to express let’s ...

So:

• Negoziamo una soluzione... = Let’s negotiate a solution...

This is a very common structure in Italian.

Because Italian usually drops subject pronouns when the verb already makes the subject clear.

Here, negoziamo clearly shows we:

• negozio = I negotiate
• negozi = you negotiate
• negozia = he/she negotiates
• negoziamo = we negotiate / let’s negotiate

So noi is unnecessary unless the speaker wants emphasis or contrast:

• Noi negoziamo, loro rifiutano.
  We negotiate, they refuse.

In your sentence, leaving out noi is completely normal.

Italian often uses an article where English might or might not use one.

• una soluzione = a solution

Here it introduces one possible solution, so the indefinite article una is the natural choice.

If you removed it, the sentence would sound incomplete or unnatural in standard Italian:

• Negoziamo una soluzione... = natural
• Negoziamo soluzione... = incorrect

Because this is a case where Italian often uses the subjunctive after a noun that refers to something wanted, sought, proposed, or not yet established.

• una soluzione che rispetti...
  = a solution that respects...

The idea is not a specific, already identified solution, but a solution of the kind that should respect the law and this right. That uncertainty or desired quality often triggers the subjunctive.

So:

• che rispetti = present subjunctive
• che rispetta = present indicative

In many contexts, the subjunctive is preferred because the solution is still hypothetical or being sought.

Sometimes you may hear or see che rispetta, especially in less formal usage, but che rispetti is the more grammatically careful and standard choice here.

The difference is roughly this:

• che rispetti: a solution that would / should respect the law and this right; the solution is being sought or proposed
• che rispetta: a solution that does respect the law and this right; it can sound more definite or factual

Because the sentence is about negotiating or finding a solution, not describing an already identified one, the subjunctive rispetti fits very well.

Rispetti is the present subjunctive, 3rd person singular, of rispettare.

Conjugation of the present subjunctive:

• che io rispetti
• che tu rispetti
• che lui/lei rispetti
• che noi rispettiamo
• che voi rispettiate
• che loro rispettino

Here the subject of rispetti is una soluzione, which is singular, so rispetti is the correct form.

Here che means that / which and introduces a relative clause describing una soluzione.

• una soluzione che rispetti la legge e questo diritto
• a solution that respects the law and this right

So che connects soluzione with the verb rispetti.

It is not a question word here. It is a relative pronoun.

In this sentence, diritto means right in the sense of a legal, civil, or human right.

That is different from legge, which means law.

So:

• la legge = the law
• questo diritto = this right

Italian diritto can sometimes also refer to law as a field of study or system, for example:

• studiare diritto = to study law

But in your sentence, because it is contrasted with la legge, it clearly means right.

Because diritto is a masculine singular noun.

So the demonstrative must agree with it:

• questo diritto = this right

Compare:

• questa legge = this law
  (legge is feminine singular)
• questo diritto = this right
  (diritto is masculine singular)

Agreement in gender and number is very important in Italian.

Because legge is a feminine singular noun, so it takes la in the singular definite form.

• la legge = the law

In Italian, definite articles are used very frequently, often more than in English. Here the article sounds fully natural because the sentence refers to the law as a known legal framework.

Compare:

• legge = law (as a bare noun, dictionary form)
• la legge = the law

Yes. The conjunction e means and, so the solution must respect:

1. la legge = the law
2. questo diritto = this right

The verb rispetti applies to both nouns together.

So the structure is:

• una soluzione che rispetti [la legge] e [questo diritto]

In other words: one solution that is compatible with both.

Yes, it is understandable and natural, especially in political, legal, diplomatic, or institutional contexts.

It means something like:

• to negotiate a solution
• to work out a solution through negotiation

Depending on context, Italian might also use expressions such as:

• trovare una soluzione = find a solution
• raggiungere una soluzione / un accordo = reach a solution / an agreement
• concordare una soluzione = agree on a solution

But negoziare una soluzione is perfectly plausible and idiomatic in the right context.

The structure is:

• Negoziamo = main verb
• una soluzione = direct object
• che rispetti la legge e questo diritto = relative clause describing soluzione

So, grammatically:

[Main clause]
Negoziamo una soluzione

[Relative clause modifying soluzione]
che rispetti la legge e questo diritto

A very literal breakdown would be:

• Negoziamo = Let’s negotiate / We negotiate
• una soluzione = a solution
• che rispetti = that may respect / that respects / that should respect
• la legge = the law
• e questo diritto = and this right

That is why the whole sentence feels compact but precise.