Does running pruning node make the initial sync faster? Does running bitcoind with -prune option make the initial blockchain sync faster or not? I know it makes it smaller on disk, but is it faster?

I keep reading conflicting information online - some state that it is quicker because you need less disk operations, some state it is about the same.
No, pruning will not make the initial sync faster. The information that gets removed by pruning isn't accessed turning the initial sync.

Currently pruning makes the initial sync somewhat slower: more frequent flushes are performed in order to allow pruning to work, and the work of actually deleting things creates its own small slowdown. About the same is probably a fair statement in general.

The only configuration which can substantially speed up the initial sync is increasing the dbcache option.  If you have plenty of memory (e.g. >4GB) making this setting larger can radically reduce the sync time, esp. if your disk is slow. For 8GB ram I recommend setting dbcache=4096 during the initial sync.