You cannot vent any condensing type appliances into a common vent. What that means is that a high efficiency furnace and a tankless type condensing water heater require dedicated vent pipes that terminate individually / they cannot be spliced together with any kind of connectors.
Tankless water heater gas pipe
Tankless water heaters require significantly more gas than the regular ones. Also, they have more restrictions as far as the gas line pressure. Navien tankless water heater manufacturer suggests to install the appliance as first from the gas meter to ensure proper operation and the natural gas line pressure to be between MIN 3.0” WC - MAX 10.5” WC.
So it would be wise to have that line pressure checked by a professional before purchasing the water heater.
The “T” installation would be fine but arranged in such way that the WH is closest to the gas meter.
All the details for the Navien water heater are here: Installation manual
and pages 21 & 24 partially cover your questions.