I have 2 different applications: say Application1 and Application2.
I have integrated Application2 with keyc
YES- You can login to the Application-1 with out using keycloak login interface.
Various client adapters are available for achieving this. here you didn't mentioned your application frame work.
To know more about the keyclaok client adapters : click here
For example if you are choosing Node.js adapter then you can follow the link : node.js adapter
keycloak implementation with node.js adapter, details about the REST api's and token validation mechanism are well explained in this link click for example