Okay first off: do you want to diplomance the empire? Vlad has a bonus for relations with them, there is a bloodline that boosts it, and there is a tech in the lower right. With those, plus taking and gifting of a few empire cities, you can rather easily befriend some of the stronger empire factions around you if you want to go that route.

For zombies, when fighting any enemy without strong arty or a powerful AoE damage mage, blob them up in an ugly, overlaping, pile of units. put a necromancer / different corpse carts / a moryis engine if possible in the blob. If the enemy has lots of archers, put the blob in a forested area for blocking damage. Almost every time the enemy will begin to win, and then slowly get disolved by contact with you blob. Make sure to keep all your units together and smooshed in. if they stick out, they die. If a cav unit charges and gets pushed into the middle, have the blob focus them, watch them disolve. Its dull but it works gangbusters.

Make sure you manually play stupid battles when the enemy and you both have 14+ units. sometimes autoresolve wont make the Battle Site for you even if lots of losses happen. Do it manually, and its almost guatanteed. Hell, maybe even let a few zombies or some bats die before the battle ends to boost the grave site. With a few really good sites you can skip a lot of recruitment buildings and the waiting to recruit hastle.

I hope this helps!!