4.11 is four years old and much has changed. The techniques described earlier are focused on v6.x and v7.x. Upgrade. Bear in mind that unlicensed copies will disable certain features. Also, due to improvements and changes in how things are done, full backward compatibility cannot be guaranteed. It's best to export with the version that created the project.
To sum up...
1. When a clip is deleted using the DEL key or a right-click|DELETE a gap will be left. Close it with a right-click|CLOSE GAP. Use a right-click|DELETE (ripple) and there will be no gap.
2. To move a portion of a clip in the bin to the sequence, first select it, then move the red line to the start. Click SET START. Move the line to the end and click SET END. Click the chevron to the right of the ADD button and choose where the clip is to be placed.
3. To trim a clip that's already on the sequence, select it, then click the Preview tab above the preview window. Mark the SET START and SET END points. The sequence clip will be trimmed without gaps.
4. Of course, a clip on the sequence can be simply split out (which creates a new sequence clip) and the unwanted adjacent clips deleted.
Trim procedures, using the SET buttons, apply to video clips, not to still images.
Check out the tutorials.