If you have dealt with the condensation, you can now clean off the surface ready for new treatment.
If there are black stains under the varnish, with is very common, you will have to abrade away the old varnish, and the top layer of the timber beneath. If the stain goes deep, and you intend to use another transparent coating, you can bleach out the stain, and maybe dye the wood to even out the colour. this is quite a lot of work.
It is quite difficult to sand off close to glass without scratching it, but you can use wire wood balled up in your fingers. As yours are stained with mould you can use a paint stripper if it makes it easier. If you think there is any decay in the timber, remove it and apply Cuprinol Clear Wood preserver to protect it in future.
Varnish is not as durable as paint, and flaws will show through it. I'd use a breathing woodstain if you want a transparent or translucent finish. Use an Exterior grade, even on the windows, due to the sun and water problems.
If you are willing to paint them next time round, you have still got to get the old varnish off, and any decayed timber, but you have not got to worry about staining.
Wait until dry sunny weather when you are confident the wood has dried out thoroughly. Once you are down to bare clear wood, I suggest putting masking tape on the glass, to avoid paint blotches that are dificult to clean off. You should let the paint, at least the topcoat, overlap very slightly onto the glass to form a seal against water penetration.
The most durable wood primer I know (and windows suffer from damp and sunlight) is Aluminium Wood primer (which dries grey, not silver). Better paint shops will have it, in a smallish tin. You will need a soft, natural-bristle brush, about half-inch to do the mouldings around the glass. You can use a 2-inch for the bigger sections.
Abrade very lightly between coats, just enough to remove any nibs, tears or runs, and take off any gloss. I recommend an oil paint system for windows, as durability is so important. It's usually best to use the same brand or primer, undercoat and topcoat. Don't take any shortcuts on windows.
During priming and undercoating you will improve your skill, and the brush will wear in, so you will do a better job of the topcoat. A brush which has been used and cleaned well paints better than a new brush. Use white spirit or blue brush cleaner. Be very thorough.