All these wounds of war now must be healed by you.
nec…nec means "neither…nor." Nec's are usually found in pairs, but sometimes a sentence will contain three or more of them: nec…nec…nec: "neither…nor…nor."
tumultum: accusative masculine singular from the 4th declension noun tumultus, tumultus. It is in the accusative because it is a direct object of the verb timebo.
hastam: accusative feminine singular from the 1st declension noun hasta, hastae. It is in the accusative case because it is the direct object of the verb timebo.
militis - "of the soldier" - genitive singular masculine. It's easy to forget that militis is the genitive of miles. Note also the position of the genitive; genitives tend to fall after the nouns they modify.
mortem: accusative singular feminine of the 3rd conjugation noun mors, mortis. It is accusative because it is one of the direct objects of timebo.
violentam: accusative feminine singular of the 1st/2nd declension adjective violentus, -a, -um. It modifies mortem, so it agrees with it in number, case and gender.
timebo: 1st person singular future indicative active from the 2nd conjugation verb timeo, timere, timui.
Literally, this phrase could be rendered, "since Augustus holds the lands," but that doesn't sound very impressive in English. We don't talk about rulers holding lands - that sounds stilted. The meaning behind the phrase is that Augustus controls (i.e. holds) many different nations (i.e. lands) under his power. The better English translation would be "since Augustus rules the world."
If you chose to translate the ablative absolute with a "when", it would be equally acceptable.
"I will fear neither the uprising nor the spear of the soldier nor a violent death, since Augustus rules the world.
- Tarquinio expulso, nomen regis audire non poterat populus Romanus.
Tarquinio expulso: Tarquinio here is the ablative singular form of the name Tarquinius, who was the last king who ruled the Romans before the Republic. expulso is the singular ablative masculine form of the perfect passive participle (fourth principle part) of the verb expello, expellere, expulsi, expulsum. This here is an ablative absolute. A good way to translate ablative absolutes is in it's own subordinating clause (Since, when, although, after...), so: after Tarquin was expelled. Learn more about ablative absolutes.
"After Tarquin had been expelled, the Roman people were not able to hear the king's name."