For renown, the ONLY reliable way I've found is doing tournaments, but running around the map finding them is such a pain because the map is so big. Sometimes you head for one and it finished before you get there, but if you keep your party light you can grind renown easily. I find the easiest way to win is with a balanced heraldic lance and a fast horse (turn weapon breaking off). Frankly after winning about 20 in a row I got bored and just cheated my renown up. After getting a city I will hold my own tournaments which should make it much easier. I hate grinding, so I will probably just cheat for renown but if you have the patience you can definitely use tournaments to get it VERY high.
Your problems 2 and 3 go hand in hand for me: I found the best solution is to be a mercenary. Fight in the Baltic or anywhere there is a lot of small conflicts, and have a party size capable of chasing down the patrols. These patrols are of 30-50 in size, spawn constantly, and are a GREAT way to train up troops and companions. If you combine it with trainer you can easily train up a hardcore fighting unit, and then you can fill it out with lower tier troops (which will level up decently if you focus on trainer).
I'll admit I'm not 100% sure the best way to tackle going from being able to fight parties of under 100 to being able to tackle those 300+ size lord armies - how the hell do you deal with those by the way??
If you feel that you have screwed up, I suggest exporting your companions using the camp menu and adjust them so that they some have trainer. Go around the map and get yourself some enterprises (anything that will give you a return in ~25 or less weeks is worth it IMO, I always buy the one that has the fastest return on investment rather in each city). If you are currently a vassal, resign and go mercenary instead. Don't be afraid to disband most of your army so that you can catch the patrols and focus on training up a core of elite troops. Hunt down tournaments when you can, or disband most of your army and focus on just doing tournaments for a while. In other words: you can always recover from a "bad" start.
Also, don't forget to send out your companions to increase your Right to Rule if you plan to start your own kingdom. I have sent out every companion I've found and it's at like 60 now.