Hi rosered,
Sorry to give you this "standard" answer : "It depends".
Ok, let me try to explain in detail.
1)
The X10 Mini is running Android 1.6 (2.1 later this month if all goes as planned).
2)
You need a third party app for now, called Bluetooth File Transfer.
It's on the marked, made by Mediaval Software, it's free.
And then the "depends" part....
IF your phone is rooted (see other threads about that) you'll be fine and pretty much can do as you like when it comes to bluetooth (and this app on your phone).
IF NOT, then there will be some restrictions.
From now on, I'll assume the phone is NOT rooted.
Using the mentioned app, you'll be able to connecto to ANY device (other cellphone, any brand and any modell and even laptops) to SEND (upload) files FROM your phone.
But that's the easy part.
To recieve files is another story.
Since the phone is not rooted AND running Android 1.6, you'll only be able to SEND files to your phone FROM another Android device running THE SAME app (bluetooth file transfer, as mentioned above).
Not so much fun since this scenario is not very likely to happen every time.
BUT, there's a workaround, as with everything on this planet.
You had it right in your question, yes you do have to use your phone to browse the other part for content, select it and download it to your phone.
But, this will only work with this app AND if the app is able to discover AND browse the other phone/laptop.
To do this, the other phone/laptop must be "discoverable" on the bluetooth net, you have to search for it from the app on your phone, select it and browse. Mark the files you want and select to download them.
This then depends on the other parts ability to share content and not only send.
(i.e. in windows you'll need to place the files in the bluetooth sharing folder, as the mini will look there for files to get from the computer).
So to sum it all up.
Yes the x10 mini can recieve and send files via bluetooth IF certain conditions are met.
For me personally I'm able to send files to the laptop (running windows 7 pro) and the phone is able to browse the "bluetooth shared files" folder on the laptop, get info about the files (even chech the crc32) but I'm not able to download files FROM the laptop TO the phone (initiated from the phone). And I'm not able to send files from my laptop to my phone. (initiaed from the laptop).
So, the best hope is for SE to include this feature in the Android 2.1 update due this month. (If for some reason they choose not to enable this android feature for any reason)
Hope this helps.
Oh, and read the how-to and FAQ for the app here:
Beginner’s Guide To Bluetooth File Transfer