Answer to first question:

Some days people don't have any leave bid, some days maybe one person who works on the morning shift and one person who works on the evening shift both have the day bid off, some days everyone who works the evening shift has the day bid off.

Whomever is making the schedule has to balance the controller availability with the minimum-required staffing numbers for that time of day.

Some facilities will let you flex in early, so you could just plan to arrive half an hour early (and leave half an hour early). If once in a blue moon you are a few minutes late due to unusually bad traffic, most managers are okay with that as long as it isn't a common occurance, in which case you need to leave home earlier.

Answers to second question:

(I have smaller suggestions that are needed, but I figure I'll try to be efficient with people's time and give probably the biggest two issues that I think everyone can get behind.)

1) Fix initial facility assignment. It's currently random and wastes a ton of time and money. If you're from a small town that has an opening in the control tower or you're from a large city that has an approach control or "center", you should be able to choose to go there (or close to there) once you graduate from the FAA academy. As it is now, the spot could go to a random person in a class behind you at the Academy who doesn't want that spot, and you go to some random place where you're miserable, waste everyone's time and FAA money while training there, then apply to transfer (and it's basically impossible to transfer when everywhere is below staffing and they won't release you), and then spend more time and FAA money training again at a new facility (and that other person who got the spot you wanted will also be wasting time and money training at a facility they don't want to be at either). There should be a way to submit a list of preferences and have an algorithm place you close to one of your top 10 choices/areas. If someone in authority asked me to develop a system/algorithm and a fair set of rules that's hard to game, I could probably do it, but it would take some work to come up with and then a lot more work to develop and test, but it would be worth it to the NAS (National Airspace System). Unfortunately such an assignment would probably go to the union for them to hand out to their buddies (Article 114 of the collective bargaining agreement).

Suggestion 1 (above) will save money and be more efficient in the long-run. Suggestion 2 (below) will cost more money initially, but should balance out in the long-run by attracting more qualified people who will be less likely to wash-out (whereas money is wasted on training people who will eventually wash-out, or quit when they realize it's not worth it.

2) Pay us more. Attract more qualified people who will be better controllers, by offering a better salary. The salary used to be better, but it has been eroded away through inflation. Pilots are getting 40% raises (over a couple of years) and we get 2% raises (well, 3.6% or so with the union contract). There are a lot less Air Traffic Controllers than pilots, and we are vital to the nation's security and economy. Qualified people who might be interested in ATC realize they can make just as much money in other industries that don't kill them mentally and physically like ATC does for the same if not more amount of money.

(Opinions are my own and not necessarily that of the FAA.)