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.
There are several ways you can make money:
(1) Build or upgrade new residential buildings. Be careful to include new residential buildings within your existing service zones so that you don't have to worry about needing too many new services.
(2) Collect taxes on the residential buildings that you have. This is much slower than other ways to make money, but over time, if your sims are happy, will provide a good, steady payout.
(3) Trade items on the global exchange. Really good rates go for items that are needed to expand city storage (ladders, security cameras, padlock), to expand map areas (dozer exhaust, plow, gear), and for doing disaster events (gloves, buttons, batteries). However, you can sell ANYTHING that you manufacture or create in a factory on the global exchange.
(4) Wait for simoleon bubbles to pop up and complete the trade that's asked for. Many times it will be for manufactured goods, but sometimes they ask for expansion items. If you don't have the items right now, you can manufacture the goods and go back to the bubble later and sell the items when you've completed the manufacturing.
(5) Do cargo shipments on either the boat or the airport. By fulfilling those items not only do you receive simoleons but also keys and other items to purchase specialized services that are unlocked later on in the game.
Also, in general, it pays off in the long run to purchase the most expensive police stations, hospitals and fire stations to encompass the largest area. Also, it makes sense to invest in better sewage, water and power options. Then you don't have to worry as much about making sure you're covered.
Best Answer
You're only allowed to have up to 3 new construction-site RZs, so in order to get more "RZ points" you have to upgrade one of them that's already been placed. And you can't bulldoze them.