1 I think you might have the automated replacements option set to on, put this slider all the way to the left so that you are buying the replacements that you can afford and need. At the moment I think the game might be spending all your WS on un needed replacements.
2 See 1
3 See 1, the game might be buying replacements that are not needed at present, or are all that it can afford. If it is spending all the WS each turn it will only have a few to spend on the next turn, it will probably buy what it can afford which will be infantry each turn as they use less WS. It will never save enough WS to buy cavalry replacements.
4 Battles depend on a lot of factors. Check the postures in the battle report, numbers of men, etc. It might give some answers as to why you lost.
5 Units only gather supply from the region they are in or from adjacent regions. As a rule of thumb supply points produced by a region are roughly 5 times what the supply level is. If it says that a region gives 5 supply, then this equates to 25 supply points. Check how much your stack needs each turn by holding your mouse over the pot icon that appears in the bottom right hand corner of the screen when you have the stack selected.
6 Not sure on this one, but in the release version there was a bug to do with group forming that was giving this message. This has been fixed in the latest beta patch.