control ac motor with SCR
Can I start the circuit with a BT151 thyristor by changing the
resistors or capacitors in the circuit?

Possibly, but it could be difficult. The BT151 has a maximum Gate trigger current requirement of 15 mA, while the TS820 only needs 0.2 mA. So to get sufficient trigger current you might have to reduce all resistor values (including the pots) by 75 times, as well as increasing C1 by 75 times. With 75 times higher power dissipation the resistors may need higher wattage ratings, which could be particularly troublesome for the pots.
Replacing the SCR with a sensitive Gate type would be much simpler and easier.

Can I use MCR100 or C106 thyristors because I can not find the TS820
thyristor?

Probably. The C106 has similar Gate specs to the TS820, so it has a good chance of working.