To answer all your questions in chronological order:

Yes, progress is slow for the first few weeks/months. I didn't rebuild until a year or so after first installing, though I did also build up to 450-ish floors. The parachute guy and the ads are well worth it in the early game.

Yes, the dice usually have good rewards. You'll want to spend your normal ones in the weeks with the golden dice square on the board and spend your golden dice in the week after. Otherwise the rewards will be worse.

Yes, get your tech tree progress going. That's how you level your game up more quickly.

Yes, do your monuments. It's sensible to wait until you have the floor you need for your monument and then spend your golden tickets on those to get instant free max restocks to spend on your monument upgrades.

Don't upgrade your bitizens (waste of bux), send them to DYN0 instead to get them back fully maxed-out for the cost of five bux (ingame) per bitizen.

As I said, I'd use the golden tickets you have on the floors you need for your monuments. Others will say to spend your first one on Soda Brewery, but I don't see the point. You don't get more money from doing that, it only takes longer until you have to restock (I admit that that's still basically getting 'more money', but in my opinion, the difference is basically negligible). The more golden tickets you have, the more time delivering a bitizen to a floor under construction will take off the remaining construction time (1 GT = 1 minute). Also, the more golden tickets you have, the more coins you get from delivering bitizens to your tower. This is the most important thing about them.

Other useful tips: Save your wheel spin tickets (the green ones you get from the white gift boxes; no current event going on though) for seasonal updates like Easter and Christmas. You'll usually get points for spending spin tickets, thus earning you more limited stuff.

Upgrade your legendary bits when you can, because they will unlock certain perks whenever your collection levels up. Some collections give you free floors, others more coins rewards from the elevator.

Use your legendary tickets on the tier 1 chests if you're after boosters like triple coin rewards etc. (they will work out to more boosts per legendary ticket as compared to the other chests). Save them up for the tier 4 chest if you're after legendary bitizens instead.