NO. One week is not enough, unless you refresh energy. Rosa needs 13 Brilliant Rays. My alt has done PRO 12 times and I have 4 BR. Think again if you really want to raise 3 Rosas to 5*.
See above.
PRO is just a RNG crapshoot. The problem is that because there are so many items on the loot table (any 4* or 5* awakening material, except SC/HC [those are bonus drops]), landing a specific one is a royal pain in the ass. And when you need 13 of a specific item.... welp.
Long term average for a BR is probably in the 0.5 - 0.75 per run zone.
What's even more funny is that the loot table appears to be specifically designed to punish players for bringing Locke into the dungeon.
All the new awakening materials are 4* rarity. Which means that Locke will bias the loot table towards the 5* drops, which are worthless as everyone has been drowning in these since Lanzelt. Further, as SC/HC are bonus drops, Locke doesn't help here either.
Gumi knew exactly what it was doing in creating the loot table for this dungeon.
At 0.5 per run, 26 runs @ 20 energy per = 520 for an average chance. The viable range based on good/bad RNG is likely between 400 - 650 energy spent for one Locke.
In other words, assuming no sleep and devoting all energy to PRO and nothing else, expect to spend 3-4 days farming this. Want to do other things in the game? Then yeah, unless you are ready to toss lapis for energy refills, expect to farm PRO for at least a week for 13 BR.