New Browse Window
Once you have the block of text you want in the Browse window, go to the View menu and choose New Browse Window. (There's also an icon in the toolbar to do this.) This will open up a separate window with your block of text in it. This should remain stable while you perform searches and other operations in the main window. Note that you can have several such separate Browse windows open, and move them and resize them as you please; and that in each of them you can click on the "footsteps" to switch between single-version and multi-version display mode.