As for the nozzle… you have an E3D Titan AeroStruder with a v6 heater-block. Any nozzle compatible with the E3D “v6” heater block will work.
But your current nozzle is a hardened-steel nozzle (rather than a brass nozzle). Brass nozzles transfer heat more efficiently (and you can run them at slightly lower temps because they transfer heat more efficiently)… but they are softer and wear faster. They are not suitable for use with abrasive filaments.
E3D makes a nozzle called the “Nozzle X” … it’s a hardened-steel nozzle with a poly-phobic nano coating. This means hot filament doesn’t like to stick to it very well and if something does stick it’s pretty easy to wipe clean (much easier than your current nozzle). I switched to this and am very happy with it.
Nozzles come designed for either 1.75mm vs 3mm filament so you need the 3mm version. They also make them in lots of extruder diameters. E.g. your current nozzle is 0.5mm but you can both smaller and larger diameters. (I went with the 0.5).
While I say “any” E3D v6 will work, there are considerations to think about if trying to go to a bigger nozzle opening. A 0.8 or 1.2 diameter extruder is … not great for use given your current heat-block. If you buy a LulzBot extruder with a 0.8 or 1.2mm nozzle … they use the E3D Volcano heat-block instead of the v6 heat-block. The Volcano looks roughly the same … but taller. It has a longer heat-path (and the nozzles have longer threads to match). This is because at 0.8mm … the filament extrusion volume is roughly 2.5x more than a 0.5mm. This means the filament is moving through the heat block 2.5x faster and that means it doesn’t have as much time to heat up. The longer heat-block of the Volcano compensates for that. But you can also compensate for that by just running the printer slower.