Need advice/help with bathroom, especially the linoleum floors

We bought our house about 3 years ago from some flippers, and while the master bathroom has functioned mostly alright, it was quickly obvious that they hadn't done an amazing job putting it together.

Here is what it looks like.

My primary concern is with the peeling linoleum, especially in the corners and next to the shower (First 7 images in the album).

Other concerns include:

• Cracks and lack of proper sealing between the shower and wall
• Lack of proper sealing between the sink and wall
• The water pipe/plate sticking out of the wall
• Lack of proper sealing between the trim and the floor/wall
• Open corner where trim doesn't reach the sink

So, my basic questions are what work needs to be done and is it something I could do myself? What are my next steps?