Despite not having a TDA2050 in your spice simulator, replacing it with a 741 tells you close to nothing about the TDA2050. Firstly the 741 isn't geared up (in reality or simulation) to driving an 8 ohm load and a zobel network comprising a 2.2 ohm resistor in series with a 0.47 uF capacitor.
To try and answer some of your questions
- High pass filters - it must have an output decoupling capacitor or your speaker will be dc grounding the output to 0V - the o/p from the device is centred between gnd and the positive supply - this shouldn't be attached to the speaker or you might damage the speaker or the TDA2050. The 2.2 uF input capacitor is needed because your input signal is ground referenced and the TDA2050 has bias voltages on its inputs that shouldn't be disturbed. It is not an op-amp despite looking like one.
- The bandwidth is in the data sheet. It says 20Hz to 80kHz on page 3.
- The strange jump (as you call it) at 12kHz is a 5dB peak in the response and is likely to do with the inappropriate use of a 741 in the circuit you've used and some peculiarity of its spice model. This is not-easy to explain but it's not likely to happen in a real 741 and the zobel network R6+C6 shouldn't be used with a 741 - this type of RC network is an attempt to linearize the impedance of the loudspeaker connected.
- Explained in (3)
Increasing the load from 8 ohm (inappropriate for a 741) to 1k ohm will make a difference - the 741 could expect to see a load like 1k but not 8 ohms.
