Are there any problems with attaching non-MFT lenses?
No, though you will not have access to any electronic/auto features of the lens such as AF, stabilization etc, you'll have to do everything manually. You need to take into account the crop factor, lenses for smaller systems like 8mm, CCTV etc may vignette or produce a circular image with black borders and the focal length will be longer on m43 body.
How can I see the image from the lens without a viewfinder? (Is it going to show correctly on the display?)
Yes, just like with m43 lenses... the light goes through the lens onto the sensor and the sensor image shows on the LCD display.
Can external lenses be used with Raynox DCR 250?
Do you mean using a non-m43 lens with the Raynox DCR 250 and attaching to m43 body? I think that ought to work, the Raynox is macro-adapting the lens... as long as the lens can be fitted to your m43 body then you can see the result of that.