Can we do a partition on the hard disk when uTorrents are downloaded halfway?

BitTorrent downloads are files, nothing more. As long as the files are not deleted, and as long as the original .torrent file exists, you can resume the download just fine.

Besides, resizing only moves the data around, it doesn't destroy anything the filesystem has. The metadata (file names, dates, security, streams) is part of the filesystem and is preserved as well.

(If μTorrent even tried to store anything outside the filesystem, it 1. wouldn't be allowed to do so, without Administrator rights; 2. would quickly become unpopular for storing data the most stupid way ever.)

Torrents are remarkably resilient. I've had files that I've downloaded with BitTorrent that I've moved from one computer/file system to another that, at some point, have become corrupted in some way. Instead of having to either cut my losses or to incur another lengthy download (the example I have in mind was a 6+GB file) all I had to do was find and re-download the right torrent and replace the file that it's downloading into with my corrupted file. Upon restarting, I triggered a recheck and uTorrent happily reported that I had 99.7% of the file and downloaded the rest.

So to answer your question, yes, you can safely move partial downloads around as much as you like as long as you keep the original .torrent file or can redownload it. And you can usually move partial downloads between different torrent apps without skipping a beat.