1) It depends on what you want. WinBoard has an option 'auto-flip view', which you can set from the General Options menu dialog, and that should be persistent between settings. It would automatically place the pieces you play at the bottom when you start a game (against an engine or on the server). If it is off, I think it just keeps the current orientation. If you are not playing a game, it doesn't know which color is 'yours', and it doesn't do anything.
If the auto-flip view option is off, then you have to control the view by hand (e.g. through the F2 key), and it will always start with white at the bottom. There is no way to remember the orientation you last used. Normally this is pointless, as you would start a new game, and there is no reason to assume it is more likely that you want to play with the same color as in the previous session.
You can alter the default such that at the start of a session the black pieces are always at the bottom. But for this you would have to edit the winboard.ini file in the WinBoard folder, and add at the end
/flipView=true
2) The rule of thumb is that doubling the thinking time increases engine strength by 50-70 Elo. Note that time is used more efficiently by the engine when you allow it some leeway in allocating time per move, e.g. by playing 40 moves in 1 minute instead of 2 sec/move. Especially Fairy-Max only uses a small fraction of the time at fixed max time per move, as it has no way to abort its thinking before it has finished a search at the next-higher depth, and must take a large safety margin to make sure that it can do that within the remaining time.
3) Nowadays Chess engines are absurdly powerful. What is 'enough' depends on your purpose for using it. Fairy-Max is good for an entertaining game where mortals still stand a chance to win. The strongest engines are about 1500 Elo stronger, and even crush grandmasters when they start with Pawn odds or an exchange down. Not much fun playing against those. But good when you want to know the absolute truth about a position quickly. Which engine is best depends a bit on what hardware you have. There is Stockfish, which runs well on a normal CPU. Leela Chess Zero might be stronger, but only runs well on a powerful graphics card (GPU). They work according to completely different principles; Stockfish through brute-force search through millions of positions, Leela by very selective search through thousands of positions, using a lot of knowledge for deciding what moves to search.
4) Yes, you can specify a 'Directory with piece images' in the View -> Board Themes menu dialog. They must contain the images as Windows bitmaps (*.bmp), but the format is not very user-friendly: for each piece you woulld have to supply 3 bitmaps: a monochrome bitmap to indicate a white background the shape of the piece (which, strange enough, as to be drawin in black in that image), and then two images for the white and black piece to be drawn on top of that. (This could be full-color bitmaps). This to prevent the background would 'shine through' the piece.
5) There actually is a newer 'development' version of WinBoard; it can be downloaded from
http://hgm.nubati.net/WinBoard-AA.zip . This is actually configured to use external bitmaps for the pieces, and only needs two images per piece type (for black and white). Downside is that these then need to be bitmaps with transparency, and that the standard Windows software for creating images (MS Paint) does not support that Windows bitmap format. Without transparency a third bitmap to indicate which part of the image are opaque and which are transparent is unavoidable.
