1 - With Charisma dealt with, and after giving him a descent Dex for ride, how should I prioritize my stats.
Strength is the most important stat for cavaliers. Since you want high Charisma, your only remaining dump stat would be intelligence. I'd not set Dex to higher than 14, even 12 should be enough to keep you in the saddle (but you might need 13 to qualify for feats).
2 - Weapon focus, the ride feat tree are a given. What would other good feat?
That depends. I don't know why you consider Weapon focus to be a given, for a PC it's only necessary for certain classes and builds. For NPCs, you might prioritize differently: choosing easy-to-run abilities over complex but superior. A GM has enough rules to keep track on anyways. If that's what you want, I'd add Toughness, Iron Will and other feats giving static bonuses to your list. Power Attack is something most PC cavaliers would pick up, and you should consider it too.
2.a - Teamwork feat, in particular, what would be good?
Depends. How do you see this NPC fighting? If its with other mounted characters, Cavalry Formation might be a good choice. Some decent that works with a mounted cavalier and non-mounted allies are Distracting Charge, Intercept Charge and Precise Strike.
3 - To archetype or not? Strategist or Daring General seem to fit.
If it fits thematically, I'd go with it. NPCs don't need to be that optimized, but they should be interesting. With that said, I'd go with Strategist over Daring General.
Daring General gives you a special Leadership feat, which is entierly irrelevant since an NPC can get allies by GM fiat.
Strategist is decent. Gives up the not-that-important Expert Trainer for the ability to better share teamwork feats. Only downside is the long preparation-time and short usage time. 10 minute preparation and only lasts ~10 minutes!? A PC could use that at the entry of a dungeon and be decently confident that the first fight will take place within 10 minutes, but other than that it's hard to use. For a NPC, though, it's very interesting. A good NPC that fights with, rather than against, the PCs should be a support character. Giving PCs perks is very supportive. And as a GM, you can rig the encounters so the NPC has the possibility to use this ability.
4- Order,how to choose the Right one?
Go with thematics. If this NPC is loyal to the duke, Order of the Sword or Order of the Lion is what you want. Both are even good choices, mechanically. Order of the Guard gives you a honorable mercenary vibe to your NPC. If your NPC has tendencies towards being a decent guy, caring about common folks, go Order of the Blue Rose. If the tendencies are towards being proud in the obnoxious way, go with Order of the Cockatrice.
Why is weapon focus necessary? Are the PCs going to fight him or something? If the son's Charisma is his highest ability score (instead of Stength), then maybe making attacks isn't the most important thing to him. perhaps shift his focus to making his troops better.
This might a good opportunity to use the Noble Scion prestige class.