1. - You're lying.
- You're telling lies.
- Which is more natural?-- 'You're lying'-- and more commonly used after a single (suspected) lie. Using either puts you in danger of being punched in the nose, however.
2. Don't get me started.
- This means "don't force me to start", right? -- No, it means don't encourage me to start (usually, talking about a favorite or hated subject)
3. I get along without you very well.
"get along" here means "live", right? -- Not exactly; get along means successfully perform one's duties and/or activities.
4. One day I'll get to talk to you.
- This means "One day I'll find a way to talk to you", right? -- Not really; it means that one day I'll have an opportunity to talk to you.
5. "broken toilet", "out of order toilet" and "not in use toilet". Which of these more natural? -- As an attributive adjective, a broken toilet. As a post-modifier, out of order: this toilet is out of order. Not in use does not necessarily mean it is malfunctioning.