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A DR-44 is a digital recorder. Connection would depend upon what mixing board you are using, specifically, and also, for what purpose - to playback from the DR-44, or to record to the DR-44 through the mixing board ?
The correct levels on both devices will be something you will have to find for yourself, inevitably - but, if you start at low volumes and work upward, you are likelier to find a satisfactory level quickly enough, than if you were to start at louder volumes and work downward, I think.
XLR cords are grounded audio cables with stereo capability - two-channel that is. What do you need to know about them?
The right microphone for the TASCAM DR-44 is a good question. It has two XLR inputs - microphones could be plugged into those, but they are more suited to the line out from a mixing board. The inputs are not high-impedance, which may affect your options of what to connect to them.
And it has built-in microphones for sure, though they are slightly prone to hiss.
There is a control app, that you may find much easier to use to change settings on the TASCAM recorder, from a smartphone, than using the TASCAM's own controls, which can be rather slow.
It depends upon what sort of 1/4" cables they are - are they XLR cables?
And, it depends upon whether you want to record TO the Tascam... or record WITH the Tascam from the mixer.
The TASCAM recorder has two built-in microphones at one end. They're obvious enough, they project from the 'top' end of the recorder.
The other end of the recorder (the 'bottom' as I see it but the manuals term it differently), at the other end from the microphones, has the two TRS input jacks. And not much else, on that end.
1/L is one of those inputs, the other is 2/R. Left and right channels in short.