If you need to buy a MOBO either way, definetly go for DDR5. If you already have a DDR4 MOBO that is compatible with your CPU, you need to decide if the extra performance gain is worth the cost. 13th gen sees an appreciable performance gain from DDR5, along with keeping your system more up to date.
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Go for DDR5 since you do not attempt a super budget build. DDR4 is outdated and DDR5 not so new anymore that they are super expensive.
If possible go for 2x8 over 1x16, but they are most of the time sold as a kit anyways. The two most important numbers are the frequency and the CAS latency (CL). Do not forget about the latter!
I think the LGA1700 socket only supports 12th-14th generation (which is why I personally went with the R5 7600). You should keep in mind that your upgrade options would be limited and the re-sale value of the 13500 will be low (people may want to upgrade from their i5 12500 to an i7 14700, but not to your 13500). For this reason you may want to consider a better CPU, but then again the 14th generation is just a refresh and not that much better.
Never go single stick.
Neither. DDR 4 is almost dead and a single stick of ddr5 is not ideal