3.3V is absolutely reliable for a high reading. No need to buffer at all.
If you can be absolutely certain of seeing 3.3V, then maybe, but it is still only a 10% margin with 5V rail. Even for a Schmidt Trigger input, it is too close to the threshold for me to be comfortable, especially when a junk box transistor will give reliable rail to rail switching.
I thought HC-SR501 modules have open collector output? That means you need a pull-up resistor to get it up to Vcc (and also that any voltage measurement when the output is not active is meaningless). Internal resistor is the most convenient, of course you can go through the effort of adding an external one if you must but it's mostly a waste of effort.
If they are open collector, then a simple pull up is all that is required. It is a logic output after all.
Open collector outputs also generally are active low.
Yes, true. However, a PNP can be used to ensure that the logic polarity remains, if the program could not / should not be amended.
as per data sheet: 0.6*Vcc. Note: if you power a 5V board (Uno, Mega, Nano) through the USB connection the actual operating voltage is more like 4.5V due to the diode drop, and a guaranteed high is at 2.7V or more.
Yes and that would certainly add some threshold margin.
In case of open collector output adding the transistor as suggested in #5 won't work; that relies on the output being a push-pull output.
Not sure why you think that is?
Sorry about the orientation of this, it seems such a struggle getting images displayed and I have run out of patience!