The first thing I suggest you do is define your tectonic plates. In case you didn't know, the Earth's crust is divided into seven major chunks which account for 94% of its surface area - the remaining 6% is occupied by smaller plates.
Each of these plates is moving, very slowly, in a specific direction. Where plates are pulling apart, there will be volcanoes. Where they are pushing into eachother, there will be mountain ranges. I could go on for quite a long time about how plate tectonics affects the geography of a planet, but that should be enough to give you a basic map.
Once you have your mountains sorted out, you can get a rough idea of the overall topography of your planet by filling in the areas in between with a gradient between mountains and plains. From there, you can work out where to put rivers - all rivers start at an area of high elevation, and move on the easiest path downwards until they reach the sea (Or in some cases, simply fizzle out inland, like the Okavango river).
Now, decide what kind of climate you want to give your planet. The hotter the global climate, the smaller the areas of ice at the poles (During exceptionally warm periods like the Eocene, there were no polar ice caps). Also, the hotter the climate, the wetter the weather, provided that there isn't too much uninterrupted land (E.g. supercontinents). In the wetter parts of the land, there will be forests, while in the drier areas, there will be grassland.
To properly determine which parts get rain and which parts don't, you'd have to map out the prevailing winds like this, but you can leave that part out for a casual worldbuilding project. In short, however, rainstorms are generated in the oceans, so if the prevailing winds are in a direction such that they blow these storms towards a certain area of land, then that place will likely be wetter rather than drier.
So, when you know which areas receive more rain, you can figure out your biomes. Basically, in the tropics, wetter areas will be jungle, drier areas will be savannah, and the driest areas will be deserts. Between the tropics and the polar regions (the temperate zones), the wetter areas will be forest, the drier ones temperate grassland, and the driest places desert again. Then, moving either north or south, there'll be a band of boreal forest, then one of tundra, and finally one of ice. Whether these last few biomes will exist depends on the climate you've set for your world.
Islands are found wherever underwater mountains stick up above sea level, so they could be found along sea mountain ranges (on convergent plate boundaries), on volcanoes (on divergent plate boundaries or volcanic hotspots, which can occur anywhere) or where continents have been pulled apart by tectonic plates.
Roads are usually found connecting settlements (which are themselves often located on rivers or by the sea) and will usually take the easiest, flattest route there. Use your topography map to decide which way has the least hilly terrain. The most inhabited place will be where there is water and fertile land. Fertility of land depends on a lot of things - perhaps the region is volcanically active and the ash makes the soil fertile, or perhaps a local river frequently floods the area with new soil.
Natural disasters have many different causes, and each cause will be more common in a certain area. Earthquakes will be found along any plate boundary, while volcanic eruptions will occur where there are volcanoes, obviously. There will be avalanches in the highest/coldest mountains, floods next to rivers and hurricanes along coastal regions bordering large, warm oceans.
That answers all of your questions except the one on borders, which is simply too complex to answer in a single post. As a tip, though, try use natural barriers as borders - e.g. mountains, rivers etc., as those often end up as landmarks between territories in the precursors to nations. This may not apply if the country has split off from another one.