I think I can help. I'm assuming you're playing Catholics at the moment.
- You can petition the Pope for an invasion, but that's difficult to pull off. Additionally, if the area you're invading is heretic or infidel, you always have the Holy War casus belli. Otherwise, you're going to have to rely on fabricated claims.
- Well, besides upgrading holdings, finding guardians and fabricating claims, you should be using your other councillors. It's also worthwhile marrying off your courtiers to introduce new stock into your court - you can get some pretty damn good statted people out of that. Also, on the Intrigue menu, you can do certain events during the year to shake things up a bit - the Grand Hunt essentially is chance at large prestige gains for gold, the Summer Fair costs a lot of gold but lowers peasant revolt risk, and the Feast basically gets everyone in your Demesne and Levy to come and eat with you for a mid-length buff to opinion (5-15, i think). After a certain point you can also do the Grand Tournament, which is much the same as the Great Hunt, but also gives opinion buffs to all who attend, and stronger buffs to the winners.
You could also plot to kill someone if it will help you, but that's tough to pull off without them being extraordinarily hated / you being loved.
-Between 1.5 and 2.0x you'll pretty much always win with leaders of similar martial skill. Terrain affects negatively and positively combat in areas, as well as mountains. If you're attacking across a river while the defenders are in mountains, you're going to suffer a big loss in combat ability while they gain about the same. This can make or break a campaign - even a huge army will take pretty heavy losses but win, in such a battle. You want the battle to be somewhere where you, or failing that no-one has the advantage.
A battle where no one has the advantage, and the leaders are of identical martial skills - will pretty much always go to the bigger army. (Very large armies suffer Attrition, where they're too large to be effectively fed and kept healthy in that region. They usually lose about 7.5% of their army size every month, which generally means it's better to send smaller blocks in and only bring them together if needed in combat.
Finally, flanking pretty much is just a random event influenced by martial skill that assists the battle. (Oh yeah, Heavy Infantry are pretty awesome. I focused on them and they win battles pretty damn well.)
-Your leaders stats, your wife's stats, and your councillors' stats contribute to many things.
Diplomacy: (State Diplomacy, when counting your wife and your Chancellor's diplomacy too)
Quoted from the wiki:
Diplomacy empowers all things diplomatic and is the determining attribute for Chancellors. A high diplomacy attribute:
increases everyone's opinion towards you
gives you prestige (0.01/month per point)
gives a boost to Cultural technology acquisition
As such it is one of your most important attributes as it helps you survive succession and reduces the chance of rebellion.
Stewardship:
Stewardship helps you manage your realm and is the determining attribute for Stewards. It determines:
your tax income (+0.02% per point)
your demesne limit.
gives a boost to Economical technology acquisition
Having a low stewardship attribute can cause several bad events to happen.
Martial:
Martial skill is an indicator of how good you are at warfare and combat, and is the determining attribute for Marshals
it has a sizable effect upon any battle you lead,
increases or decreases the strength of levies you raise.
gives a boost to Military technology acquisition.
Intrigue
Intrigue is a measure of how good you're at plotting and avoiding plots, and is the determining attribute for Spymasters. The higher your intrigue:
the harder it'll be to plot against you,
the less likely you are to be discovered when plotting.
increases base plot power
It does not give any technology boost.
Learning:
Learning is a measure of your character's knowledge and is the determining attribute for Court Chaplains.
A high learning attribute gives:
Piety (0.02/month per point)
a boost to all technological acquisitions.
There are also two hidden stats, "Health", and "Fertility". Health starts off usually at around 5.00, and is dropped by injuries and illness. A high Health stat ensures old age and disease resistance.
Fertility starts off at a base of 50%, and is boosted or dropped by certain traits. Lustful is a significant bonus, homosexuality drops it, celibacy puts it to 0%. It's used to determine when or how often your wife (or you, if you're a female) can get pregnant. Both parent's fertility is checked, so a gay king married to a lesbian queen will probably struggle to produce a child, where a lustful Midas Touched pair of parents will probably be popping out babies until they can't anymore.
-Some traits are not removable, but Craven is. Craven is removed by doing risky things like the Grand Hunt, the Grand Tournament or fighting alongside your men in wars. Lustful is a great trait to have if you need a big dynasty, so most people don't remove it.
-While you're still learning, it's wise to leave taxation untouched until you're good at keeping your vassals very happy.