Yes, Mendeley does offer export - BibTex, RIS, and EndNote XML.
The search is pretty decent, though I often find I use Acrobat search instead - its word-stemming seems better.
Batch replacement is very weak - the only way to do it is to go into the database yourself and tweak it. Very unsatisfactory. There is some batch update, in that you can select several papers, and add the same metadata to all in one go: but that's not the same as a batch search & replace. The one batch search & replace it does do very well is that when you get two versions of an author's name, you can drag one name onto the other, and all the papers will get updated accordingly.
I've also found the technical support to be very slow, and often unsatisfactory.
The auto-grab of references from the web is patchy, and you may find you're often correcting it. Often, its guesses seem utterly bonkers, like it's just grabbed a few general words from the title, and gone off to find the closest match for those, in some subject that's completely alien to me.
The interface is klutzy, though I've yet to find a reference manager that had an interface I did like.
Earlier versions of Mendeley did occasionally corrupt the metadata, doing things like swapping round the lead and second author - unbelievably frustrating. This may have stopped now - I don't use Mendeley so much any more, because of this and other problems.
Mendeley does have its evangelists, and it seems to have been very slick at cultivating its fanbase - more resources seem to have been spent there than on the software. The feedback forum has now become pretty much unusable - there are plenty of important things in there that have been "planned" or awaiting assessment for 2 or 3 years.