We build web applications in a rigrous and structured way as follows: 1.Requirement gathering 2.User Flow 3.Wireframing 4.System Design 5.UI/UX Design 6.Coding 7.Testing
Broadly speaking, we use MongoDB, Express, React and Node.
Yes, we do work only on UI/UX design as well.
Typically for small apps, nearly a month is needed to build it. It totally depends on the scope of work involved.