How to earn epic points when no epic project is available

The game uses your device's clock. It subtracts the time you started from the current time to determine if a timer should have completed when you restart your game. If your device time is changed this will be reflected. For example, if you advance your clock, then timers will be reduced by this amount. DO NOT DO THIS, it only works if offline, and when you go back online it will rollback your game.

I have timed this myself, because I felt the same way, and they do not advance any faster or slower when playing online. There is sometimes a case, similar to what you mention, when you play offline for a while, then play online, it will resync the game play (and may even rollback your progress), this has happened to me.

Be aware that if you spend a lot of time offline/out of service the chance of desync and rollback increases. Most mobile phones and tablets have terrible chronometers that will lose time often a much as 1 minute per day or more. They depend on cell service and WiFi to set the clocks periodically. If you find you have frequent rollbacks or timers that take a while this is something to be aware of. Some cell phones only set their clock when calls are received, so even if it's on if you don't receive calls or messages your clock may be off and this will affect the games times as well.

In order to unlock the modern looking luxury skyscrapers, you need to have a sufficient amount of specialty services available for your sims. This includes (in addition to parks) schools, transportation, casinos, landmarks, etc.

You can determine which areas are candidates for the modern skyscrapers by clicking on the "Wealth Forecast" (looks like a hard hat icon) under the residential tab. The dark orange buildings will upgrade to Luxurious Homes.

If your current buildings haven't finished upgrading, by adding enough services to the area, they will become luxury buildings by the next upgrade. Otherwise, you have to demolish the old buildings and start over to get the luxury buildings.