The only things you'll manage within two weeks on that list is the main scenario quests and maybe MAYBE (if you get good groups in the DF/PF) the extreme primals, but considering you haven't done Titan yet I wouldn't hold my breath.
Getting the nexus within the next two weeks is also nottu gonna happenu, because Alexandrite is one guaranteed daily and if you plugged away at it all day you could maybe - maybe - get around 8 with the new fate drop rate. I'm talking dungeon, hunt and fate grinding every minute though, doing nothing else. Upgrading to Nexus is another matter entirely because that requires getting 2000 light and the max you can get from a single encounter is about 32, and that's from the hardest stuff in the game.
As for getting the classes to 50 - it'll take at least a couple of days to get a class from 1-50, but that's a great one to work on.
In short, that's very unrealistic. What you just listed would take months of non stop playing, and it would take playing the game very economically (i.e. not idling while waiting for dungeons) etc. However you should definitely work toward all of those goals.
Take it from a person who is unemployed and recovering from surgery. I have been playing this game for on average about 8-10 hours per day since I re-subbed a couple of weeks ago, and I've been playing it a shit load. I've done all the main story content, I've yet to beat Shiva Ex, I'm still upgrading to the Novus, my WHM is level 32ish, my WAR is level 47, PLD is 22, ACN is 15, PUG is 15, and all the crafting classes are 15. Remember aswell that levels 40-50 take about as long as 20-40, and that's even with the new dungeon exp and fate grinding between it.
You do need to spend more time playing though, you're missed <3
. I sorta did DPS after we concluded that three tanks pulling aggro isn't working, and it was pretty bad, 
