Syncrometer parts
Given the technical focus of Indian secondary education, I'm surprised that you don't have some hobby shops or Radio Shack's (or equivalent). Check with your local schools. They might have a
Science lab or electronics club which knows where to buy individual components. Also, there are a number of Australian electronics websites with components.
In a circuit with so few parts, everything affects the oscillator frequency. However, some affect it more than others. The .1uF capacitor's main function is to protect the transistor from inductive spikes. The .01uF capacitor is the one which you might have to change with different transformers. Digi-Key has a capacitor kit which has way more than you need, but is the only kit I could find with the right range of values. Part number is P4542-KIT-ND, for $50. It will be cheaper to buy little 10-packs of a few different values.
For the transformer, the original has an EI-19 core size. The next size up, EI-24, should work with very little tweaking. Here are some transformers which are approximately equal:
Radio Shack 273-1380, 1K CT primary, 8 ohm secondary
Mouser 42TM013, 1K CT primary, 8 ohm secondary (made by Xicon) - best starting point
Mouser 42TM008, 800 ohm CT primary, 8 ohm CT secondary (made by Xicon)
Mouser 42TU013, 1K ohm CT primary, 8 ohm CT secondary (made by Xicon)
Mouser 42TU008, 800 ohm CT primary, 8 ohm CT secondary (made by Xicon)
Mouser is an excellent US distributor which has no minimum order quantity on standard stocked parts. They also have a huge selection of capacitors.
Asia/Australia Sales: asia@mouser.com
Let me know if this helps.
ak