Small voltage (<50V) Schottky-diodes can be regarded as having zero reverse recovery time (as there's nothing to recover from), so in this sense, they are faster than any fast or ultrafast diode. Larger voltage Schottky-diodes have some additional and parasitic structures, which may show some reverse recovery-like effects. Schottky-diodes also differ from regular diodes in that their forwarding voltage is smaller.
As long as your circuit does not require diodes with a higher voltage rating, Schottky-diodes are a perfect choice for any place where a fast diode is required. Therefore 1N5819s may substituted in place of the UF4007s in this circuit. 1N4148s are also acceptable for this circuit (even though being normal diodes, they have a very small reverse recovery time), and they are also available almost everywhere.
There are two roles for the C1/C2 bootstrap capacitors: they have to store charge while the bootstrap diode is reverse biased, and they have to provide this charge to drive the upper MOSFET gate with a sufficiently low impedance. Electrolytic capacitors are usually not enough for the latter role, that's why C2 is present in this circuit. The optimal choice for this role is a small, SMD ceramic capacitor with a very low impedance (0805, or even smaller X7R-type), connected with the shortest possible traces. On the other hand, the charge storage necessitates a certain minimum capacity, depending on the gate charge of the MOSFET and the switching frequency. For a MOSFET with smaller gate charge (like the IRF540), a 470nF..1uF capacitor is probably enough, and since this capacity can be provided by a small enough SMD ceramic capacitor, C1 & C2 can be combined in this case.
To relieve the burden on the body diode of a switching MOSFET, a sufficiently fast diode with a sufficiently high voltage rating and a low forwarding voltage is to be used. Again, Schottky-diodes are a perfect choice for this role, as long as their voltage rating is okay. So you may use MBR1045s in this circuit.