OK, I can only base my comment on the information in front of me. Just for clarity, this Particle sensor is actually a Particle Transducer that contains a Particle Sensor. The Transducer takes the output from the sensor and transforms into Digital values of a Pulse Width Modulated signal, and a UART output, but the resolutions of these could be different.
The UART spec seems to indicate that the Resolution for the spread of the particle concentration is 12 to 13 bits (high byte * 256) + (low byte / 10). However, the Maximum sensitivity used from the sensor appears to be 0.3ug/m^3. For a maximum concentration of 999ug/m^3, this needs 4096 values (to be able to create up to 3,333 discrete values). 4096 values requires 12-bits, so I guess we can say that the UART has 12-bit resolution.
To answer your questions
The UART transmission rate is 9600 baud so the bit width is 104us, which means that you would need a Data Acquisition device that can sample at a rate of 4us to be able to recreate a good representation of individual data bytes. So the minimum sample rate that you can use would be 250kHz . If you're only making 5 captures every 180 seconds then it would be better to Trigger only when there's a waveform available. So, you could use a PicoScope 2204A and set it up to capture 1 seconds worth of data, once triggered by a start bit, and then save the 5 buffers of data every 180 seconds (using an alarm).
The Schematic for the output of the PWM seems to indicate that the resolution of the transducer for the converted output from the sensor, in the PWM is 1ms for every 1ug/m^3 of particle concentration. So, it appears that the resolution of the PWM is 10-bits, but even if was 12-bits the PWM has a much larger individual bit size than the UART, so you could also use the PicoScope to capture the PWM waveforms. However, if you want to capture both the 1um and 2.5um PWM output waveforms, along with both the RX and TX ports of the UART then, as the PS 2204A only has 2 Input Channels you'd need either 2 PicoScope 2204A's or a 2207B MSO (if the UART output and PWM output need to be synchronized and captured to the same data file), which would be the lowest cost devices that we have available for sale, with 4 Channels. The MSO allows you to capture Digital Signals as well as Analogue signals, so with it you can capture either the UART or PWM waveforms on 2 Digital Channels, and the other waveforms on 2 Analogue channel (my recommendation would be to use the Digital Channels for the PWM, as its switching at a level that can be easily accommodated).