1
After trying several keys, I succeeded to open the front door.
After trying several keys, I succeeded in opening the front door.
After trying several keys, I managed to open the front door.
Use succeed in + -ing, not succeed to + infinitive, to say that you managed to do something. You can also use manage to + infinitive.
2
She wants to succeed her first job.
She wants to succeed in her first job.
When you say what someone wants to do well in, use succeed in + noun: ‘She wants to succeed in her first job.’ Do not put the noun directly after succeed with this meaning.
Succeed in is a verb + preposition pattern.