Fortunately it’s the same answer for both questions. For a chance at master writ drops, you have to be level 50 in the craft and doing max level daily writs. This means the first passive in the craft must be fully unlocked.

After that, there are several areas that you can improve your modifier on a master writ dropping in the daily writ reward coffer:

1. Achievements - Having as many achievements as possible cleared in the crafting profession. For example, having knowledge of the hakeijo essence rune is an achievement in enchanting. Knowing it will improve your chance of an enchanting master writ drop.

2. Motif Knowledge - Having motif knowledge of FULL (all 14 pages) purple and gold motifs will also improve your chances for equipment master writ drops. This excludes crown store only motifs ... such as Grim Harlequin and Frostcaster. Start out by learning the easy purple ones first (e.g. Primal, Ancient Elf) and proceed from there.

3. Trait Research - Having traits researched will also help improve chances of equipment master writ drops ... up to all nine (9) traits reasearched for the best modifier.

4. Provisioning Recipes - Purple provisioning recipes learned will help the chance of possible provisioning master writ drops.

You can still sometimes get a master writ with a completed max level writ and none of the above items cleared ... it’s a random drop after all. However, taking care the above items will certainly improve your chances greatly.