To add a dissolve you would want to add keyframes to the opacity property for the image. Park your playhead at 10 seconds and with the image selected hit the letter t. You should see the opacity property for the layer. If the stopwatch isn't blue then click it, which will turn on animation for that property. Go to the time at which you want to end the dissolve and wind the value down to 0. You should have two new keyframes on the opacity channel, and the layer will fade out.
A wipe can be achieved in many ways, one of the simplest is using a mask. With the image layer selected hold the alt / option key down and double-click the quickmask icon:
That will add a rectangular mask the size of your layer. Hit the m key to show the masks for the layer. Park the playhead at the time at which you want to start your transition and click the stopwatch next to the mask path property to animate the mask, tThis will also make one keyframe.
Now move the playhead to where you want the transition to end. Double click on the mask outline in the comp window, and you should see a wireframe outline around it. Drag the wireframe right off the screen, in the direction you want the wipe to go. Hold the shift key to constrain the movement to vertical or horizontal only. This will create another keyframe, and the layer will wipe off.
You can add easing to the keyframes to make the motion more pleasing - hit the f9 key to add ease-in/out. You can further refine the motion in the graph editor (hit this button with the mask property selected)
As for anything in After effects the ways of achieving these effects are limited only by your imagination and skill. Hopefully using native AE tools instead of relying on presets will give you a taste for how it works.