Connecting multiple DC sources in parallel without the use of diodes
Actually when multiple dc sources have to be connected to increase the current, the problem is not as simple as it looks.
First, you have to look into the actual problem which stems from basic electrical principle, ie.,

Different rating Voltage Sources should not be connected in parallel and Current sources should not be connected in series.
What is acceptable is like this: One controlled voltage source fixing the parallel combination voltage and other sources behaving as current sources.




simulate this circuit &ndash; Schematic created using CircuitLab

Droop control is usually employed in parallel combination of voltage sources.(You can check the literature for that). Most commonly, it is used in grid where multiple sources are connected.

So, the problem comes down to a basic one. We have to control the dc link using one source acting as voltage source and other sources to behave as current sources(if more than one acting as voltage source, control problem comes into the picture with possibility of circulating current).
This implies we would need, a voltage to current converter (Power electronic circuits have to be dealt with). Now this becomes a little complicated in which you will have to study up a bit on it. It is difficult to tell all the things here.
Following are the references you can read in which they implemented such a thing:
Unitrode IC Application Design
FE Industrial Application
Many more available on internet.
The questions that you asked:

Connecting only via schottky diode won't solve your problem. Since then only 1 voltage source will be providing power.
For the case of MOSFET's circuit that you have shown, same thing applies