"Alone" means without or separated from others.
- He lived alone for two years before he met his wife.
"Lonely" means unhappy because of being alone.
Only / Unique
"Only" expresses singularity, not more than one, in a specific time or place.
- He was the only student in class on Friday.
"Unique" adds that this singularity is extraordinary, exceptional, unequaled.
- He's the only player to win the tournament five times in a row.
- Nobody else has been able to accomplish this.
- He's truly unique.
Exercise: Alone - Lonely - Only 1