Bandwidth depends a lot on the materials used to build it; a j-pole made of 2" diameter copper tubing will have more bandwidth than one made out of 300 Ohm twin lead, but they are both "j-poles."
Use any sort of coax to feed a j-pole. Obviously, 50 Ohm coax is preferred since most of our rigs and test instruments are designed for 50 Ohms. The "fatter" the coax is, the less loss it will have.
The SWR of a j-pole is up to *YOU*, and not the manufacturer. J-poles have an adjustable matching transformer built into their designs, and that can be adjusted at any time in the field by moving the feepoints on the two vertical elements up and down. So, you can make the SWR whatever you want it to be, and make it "dip" at any frequency you want -- by your own adjustment.
Normally, a j-pole will cover 2 MHz of the two meter band with a reasonably low SWR (like 1.5:1 or so). You select which 2 MHz you want it to cover! Although any antenna can be used on any mode, normally a j-pole, being a vertically polarized antenna, would be used for FM work only (including voice and packet) because SSB-CW operators (and ops using other digital modes besides packet) are using horizontal polarization. There is a great deal of "cross polarity loss" when you use a vertical antenna to contact horizontally polarized stations, so for SSB-CW work, it pays to put up a separate (horizontal) antenna.
WB2WIK/6