I work in a big company and we decided to program our programs ourselves and not let them be done by external companies. Any tips for my team and me? My programming skills are quite good, those of my team members a little rusty. We only ever made the application design.

My ux teacher said, forgotten stakeholders are forgotten requirements. And I think he's right. So take a walk through your company and talk to the users... Prototype often and do user testing.

Remember one false design decision could be easy cumulated into a human life worth of time wasted.
Hire a UX Designer...

build an easy way for users to write feedback.

There is a great way for gathering requirements its called Object Oriented Design.
https://goo.gl/Z6x1z8
Object-oriented design - Wikipedia