Junior base: EWR. They advertise you can get any base you ask for, but they have a history of changing everyone in a class to EWR. They offer generous commuter policy so your hotels are paid for.
Vacation: 2 weeks after 1 year, 3 weeks after 5 years.
Leave: You can ask the Chief for unpaid leave and it's usually granted. They'll deplete your sick time, then your vacation time, and terminate your health insurance at the 30-day mark (they don't want to, it's just their policy to keep their costs down). You can take unpaid leave indefinitely, but they'll pretty much terminate you at 30 days unless you go FMLA or get an LOA, to make sure you're not running up a health insurance bill.
For having a baby, you either need to be friendly with the Chief, or just call off sick and use up sick time/get marked no-show/refusing to fly when called by scheduling, and deal with the fallout later. They don't fire you for going below your allotted sick time.
The last two questions depend entirely on whether you're FO or CA/DEC. FOs are currently overstaffed, so you will not fly much at all at the bottom of the list. As Captain you will fly 4 legs every day, including your days off, and you'll have 11-12 days off a month or less.
Over the last year, post-covid, very few new-hire FOs have stuck it out to get the hours to upgrade or flow, they leave while in training or shortly after finishing IOE and getting on reserve for a few months, when they realize they rarely get called to fly. Most new-hires go Spirit/JB/Flex/whatever when they realize they don't have Captains to fly with at Gojet, and thus will never build the requisite hours.
The rare breed of FOs that are upgrading have been with the airline for a long time due to living in base or being close to flow in Aviate. But there's a large group of senior/lifer/experienced First Officers who are waiting on Aviate and NOT upgrading (the upgrade checkride is a big risk due to a poor training footprint/program), which is taking all the flight hours away from new-hire FOs, and contributing to their gridlocked career progression for new-hires.
Basically, until CA/FO ratios are in balance, Gojet is a dead-end for new-hire FO and a lethal workload for Direct Entry Captain. There's no quick fix or quick turn-around, they need to lose a bunch of FOs to Aviate/other carriers and shrink significantly before a new-hire FO can have the standard career progression at Gojet and CA Quality of Life return to livable.