It can if you follow it with a complete thought. Here are examples:
To save some money, he packs a lunch at home instead of buying fast food.
To make herself feel better, she called her best friend.
To improve her grades, she has hired a tutor.
To arrive at work on time, I need to be out the door by 7:15 am.
we all started at the same time
I started to work out two weeks ago.
nothing
The sentence is correct if you and the article 'a': "She started her journey a long time ago."
"has started" is the simple predicate.
Yes, it is.
A simple predicate consists of only a verb or verb phrase. In this sentence the verb phrase is -- has started
"Has started" is the correct verb to use in this context. The sentence should be written as "The weekend has started."
She jumped the gun. She started at 3, when the other started at GO!
No, but you can make a sentence with the word suddenly. Suddenly it started to rain.
he started to accelerate.
Suddenly.