Now Google Drive has a feature called “filter views”. It makes some filters available only to you while you don't change any data.

Use filter views in the new Google Sheets

In Google Sheets, filtering your data makes it easier for you to view and analyse data by letting you hide data that you want to temporarily take out of view. The new Google Sheets introduces filter views as well, which allow you to create, name, and save filters that you can use without disrupting how others are viewing your spreadsheet.

Creating a filter view

When you create a filter view, it’s like saving a filter that you can use over and over again.

1. Open the spreadsheet where you would like to create a filter view.
2. Click the Data menu, hover over “Filter views…” and select Create a new filter view. You can also click the down arrow to the right of the filter icon and select Create a new filter view.
3. Using the down arrows in the column headers, sort and filter the data to fit your desired view. Your filter view will be saved as you make changes.
4. To close your new filter view, either click the X in the top-right corner of the spreadsheet or click the down arrow to the right of the filter icon and select None.

(Note: If you had existing shared filter on columns first remove that.)

Source.

Overview

The OP basically wants to be able to use the spreadsheet functions over the original data without having to scroll across a large number of rows and columns. His background make him think about having custom views and a easy way to change from one to another but Google Sheets doesn't have a built in feature to manage custom views.

Fortunately the fourth requirements are doable by using built-in features and Google Apps Script

Rows could be hidden by using filters but columns only could be hidden manually or by using code.

For 1, and 2 use Google Apps Script to create custom menus that apply the hide/show columns and optionally rows over the "master sheet". This will allow the user to edit the data directly over the "master sheet" and sort it.

Code example

The following code creates a menu for handling the hide/show operations of columns specified in a global variable.

var cols = [1,5,7]; //columns to be hidden/shown

function onOpen() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var menuEntries = [ 
    {name: "Hide", functionName: "hideCols"},
    {name: "Show", functionName: "showCols"}
    ];
  ss.addMenu("Custom Views", menuEntries);
}

function hideCols() {
  var sheet = SpreadsheetApp.getActiveSheet();
  cols.forEach( function(col) {
      sheet.hideColumns(col);
    }
  )
}

function showCols() {
  var sheet = SpreadsheetApp.getActiveSheet();
  cols.forEach( function(col) {
      sheet.showColumns(col);
    }
  )
}