Generally yes, because heat spreads evenly instead of concentrating on hot spots that carbonise liquid and cotton. Two to three weeks is a normal mesh lifespan where old wound coils managed one. Priming still matters; mesh forgives many sins but not a dry first fire.
Barely, at this point. A few legacy tanks only take wound coils, and some MTL purists prefer the slightly warmer, slower character of a classic round wire. For everyone else mesh is simply the better default, which is why manufacturers moved wholesale.
Follow the printed range as ever, but expect mesh to perform well at the lower end of it; the extra surface area does the work that brute wattage used to. Liquid rules are unchanged: thin 50/50 for high-resistance mesh, thick shortfills for sub-ohm mesh.