If you have the basic version, I don't know what all it can do, but you should be able to add a mask to the timeline and give it a chromakey alpha.
You need to make a B&W mask of a rectangle the size that you want to use and feather-edge it. In the image below, I created a 1920x1080 rectangle in Xara, gave it 100% feather edge, and exported it to jpg. Then I imported it onto track 2. My image or video is on track 1. Select the mask, Effects, Video Effects, Chroma Key, and click on Alpha. You may have to invert the arrow (it should be pointing downwards) at the left of the mask object if all you see are the edges of the image on track 1.
Here is what the resutl looks like.
If you want a different colour in the feathered area, add in a coloured rectangle to track 3. I added in a red rectangle for the image below.
Alternatively, you can inverse the order of the images, putting the photo or video on track 3 and the red background on track 1. In this case you would have to invert the arrow of the mask so that the photo shows in the black part, and the background in the white or lighter area.
You can find a series of masks that comes with MEP under:
C:\ProgramData\MAGIX\Movie Edit Pro 2015 Premium\VideoEffects\EffectAlphaMasks\HD
If you can't access ProgramData, you will have to unhide it in Windows Explorer.
Here is a tutorial that explains another method about using mask with effects, but I don't think that the feature is included in basic, only Plus.
Do you have the basic version or Plus? Did you download and install all of the Extra content?
There is no blur edge command. The only ways that I know of are to use a mask or another edge object. You can blur the edges using a similar type mask and follow the instructions in the tutorial.
Or, and you may not have all of this if you only have the basic version, go to Effects, Design elements, Image objects, Border and select a frame, like Frame 1 and drag it onto the video. It will appear on track 2 (or 3 if you have the audio on a separate track). Select it on the timeline. Go to Effects, Video effects, Color, and drag the Saturation slider to the left to -100. This will make the border black and white (gray). With the border still selected, under Effects, Video effects, Sharpness, apply Artistic blur to suit what you want. You can try different borders until you get one that you like.