The impression I had was that we were leaving the West and entering the East. (1.1)
Harker considers Budapest, the capital of Hungary, to be the last outpost of "the West" as he enters "the East." It's a total cultural change after crossing the river—in the "East," everyone is superstitious and caught up in traditions. Also, there are vampires.
In the library I found, to my great delight, a vast number of English books, whole shelves full of them, and bound volumes of magazines and newspapers. (2.28)
Dracula learns about Englishness by reading English literature. Just another thing that Dracula and non-English Shmoopers have in common?
"Well I know that, did I move and speak in your London, none there are who would not know me for a stranger. That is not enough for me. Here I am noble; I am boyar; the common people know me, and I am master." (2.34)
Dracula realizes that he'd be easily picked out as a foreigner in London and he just wants to blend in. It sure makes hunting easier when folks don't realize you're a vampire.
"I long to go through the crowded streets of your mighty London, to be in the midst of the whirl and rush of humanity, to share its life, its change, its death, and all that makes it what it is." (2.30)
Of course Dracula wants to be "in the midst of the whirl and rush of humanity." He'd be like a kid in a candy store! So many people to feed on, so little time. That's the trouble with Transylvania—there just aren't enough people.
I began to look at some of the books around me. One was an atlas, which I found opened naturally at England, as if that map had been much used. (2.50)
The atlas of the world opens "naturally" to England, as though England were the only "natural" choice for Dracula.
This was the being I was helping to transfer to London, where, perhaps, for centuries to come he might, amongst its teeming millions, satiate his lust for blood, and create a new and ever-widening circle of semi-demons to batten on the helpless. The very thought drove me mad. (4.62)
Jonathan imagines Dracula invading England and glutting himself on the blood of English people. He feels powerless to stop him, and imagines that the English will be likewise "helpless" against the vampire.
Dr. Abraham Van Helsing
"He has all along, since his coming, been trying his power, slowly but surely; that big child-brain of his is working." (23.4)
Van Helsing assures the rest of the Crew of Light that even Dracula's brain is different from theirs—it's a "child-brain."
I have told them how the measure of leaving his own barren land—barren of peoples—and coming to a new land where life of man teems till they are like the multitude of standing corn, was the work of centuries. (24.12)
The simile here is probably deliberately ironic—comparing the people Dracula wants to feed on with delicious corn is too good not to have been on purpose.
Dr. Abraham Van Helsing
In his life, his living life, he go over the Turkey frontier and attack his enemy on his own ground; he be beaten back, but did he stay? No! He come again, and again, and again. (24.15)
Dracula has always been persistent. In the past, he's invaded other countries, and Van Helsing uses his knowledge of history to help predict what Dracula will do now.
Thus are we ministers of God's own wish: that the world, and men for whom His Son die, will not be given over to monsters, whose very existence would defame Him. He have allowed us to redeem one soul already, and we go out as the old knights of the Cross to redeem more. Like them we shall travel towards the sunrise; and like them, if we fall, we fall in good cause. (24.12)
Because Romania borders on Turkey, Van Helsing compares their mission with the old Crusaders, or the "knights of the Cross," who traveled east ("towards the sunrise") to Jerusalem to "reclaim" it for Christians. Van Helsing believes that they're on a mission from God.