1) You can't really change it to a "dass" subclause. "Dass" is used for subclauses that report a fact (or similar). But "zu + Inf." is for subclauses that contain a goal or purpose (or similar). And "versuchen" (to try) is always about a goal or purpose, never about a fact, so you can't use "dass". You can change the verb, though: Sie sagen, dass sie ihren Streit beigelegt haben. Note the use of Perfekt for a completed action. 2) Again, it's difficult to change a subordinate construction into a parallel construction (two main clauses). The meaning won't be the same. If a change of meaning is ok, you can replace the subclause by a pronoun: Sie legen (vielleicht) ihren Streit bei. Sie versuchen es (zumindest).

'versuchen' is one of the verbs which have as their object an infinitive sentence with zu: versuchen etwas zu tun. It can't build a secondary sentence with 'dass'. It is just a grammatical problem, not one of the content.