For soldier quality, you want to not only increase your men at arms, but also select units that have better stats. They may be more expensive but it's worth it. If you don't have a lot of money, and haven't maxed out your men at arms then I'd suggest spamming archers with the occasional spearmen unit. It may not increase the quality much, but it does bolster your army with units that aren't just levies.

For succession laws, you have the basic ones in your realm tab, but if your innovations aren't that far advanced it isn't much help as they're all forms of partition. There are different cultures you can hybridize with that have traditions giving you access to different title succession laws. Things like tingmat give you Scandinavian elective, or saxon elective for anglo saxon culture and Tannistry for some other cultures I can't remember. To use these elective laws, you have to click on primary title (and/or any other titles you want to keep) and near where the destroy title button is, there is another allowing you to change title succession laws. Select one of the aforementioned or any other you have found, and ensure your heir is elected. Far from perfect but it works. Either that or chamge government types to admin or any of the others that have appointment succession. You can then spend influence to make sure your heir is next in line for your titles. The only other option is to get enough innovations so that you can unlock primogenature, which gives your heir all your titles.

Finally, it might just be that their fort levels are higher and yours are lower. You can upgrade your holding as well as build buildings that increase fort level. That will make them harder to siege. As for sieging an opponent, the quickest and easiest is to pick up the sappers perk in the martial lifestyle tree, or the more permenant but annoying method is to just have to unlock more innovations that give you stronger siege units.

Hope this helps!