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Q1. I want to bevel the edge. When I bevel and make loopcuts some extra geometry is made.

Q2. I have just made a simple geometry. I can't create loopcuts. I have removed doubles, recalculated the normals, yet I can't make loopcuts.enter image description here

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That geometry won't be beveled as expected because you're trying to do that on non-planar Ngon consisting of 8 vertices:

screenshot of Ngon won't be beveled

Instead dissolve unneeded vertices, and join those on the left to make solid corner:

screenshot of converted Ngon

The selection on the screenshot is an added loopcut which is better to create to avoid Ngon in the middle (however one from the right side is left which is also best to avoid).

Then there won't be any spikes because the corner will be bevelled equally in all directions.

See also related posts - Bevel tool creating intersecting faces, Can't bevel an NGon

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