I have a layer with several shapes and from here I want to delete the lines. I tryed Toggle editing and Select features by polygon but when closing the polygon, it dissapears. Also I tried to delete all the nodes that I don't want by selecting them with the Node Tool buton, but nothing happened. What do you suggest me to do?
This is my example: 
Answer
Your shapefile contains a multipart single feature as mentioned by @HDunn. In order to delete separate polygons, you will need to convert this to singleparts by using the Multipart to Singleparts tool:
Vector > Geometry Tools > Multipart to Singleparts.
I ran this and saved the output as "Free space v2.shp". Now you can edit and delete those pesky polygons!
I noticed there's quite a few of those dangles in your layer. A good method may be to use GRASS's v.clean tool with the rmdangle option to remove them automatically. You can access this from:
Processing Toolbox > GRASS commands > Vector (v.) > v.clean*
I used the following parameters (note the fairly high threshold):
Before being cleaned:
After being cleaned:
If there are any more polygons you don't want, you can remove them manually as there should be a lot less of them now.
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