1
I would like to contact with her as soon as possible.
I would like to contact her as soon as possible.
When contact is a verb, use contact + person, without with. When it is a noun, we can use contact with: ‘I am still in contact with her.’
2
It is important not to lose the contact with the real world.
It is important not to lose contact with the real world.
Use lose contact with + person/thing, without the, to mean ‘stop communicating with or being connected to someone or something’.