@Martinet welcome back to cycling! Just because an ebike can go faster than you could by pedaling alone doesn't mean you have to go that fast. Start with gears that would be comfortable for you to pedal without power and get used to the new (and pleasant

) sensation of ebike riding. The motor and battery will work better and longer if you do some of the work when starting after a stop instead of just gunning a throttle. On hills, use those easier to pedal gears and work with the motor to climb. If the motor starts cutting out on a hill then you might be pushing it using to much power and not enough pedaling. This can cause overheating and temporary motor cut out, so ease off the throttle a bit, especially if you're riding on a hot, muggy day.
I'm a big fan of front blinky lights, too. Especially in city riding where cars don't always see a cyclist. Ebikes are supposed to be legal as a bike in all 50 states according to federal laws; however, there are some cities where trail or park roads may be limited, so check with a local ebike dealer to clarify this. Mostly, trail riding and bike lane riding are governed by common courtesy, same as with a regular bike particularly if the trails or lanes are also used by walkers and runners. Depending upon the style of electric bike that you have, jumping a curb might not be the best option for you or the bike. Personally, I use the curb cutouts or gently ease the front then rear wheel over the curb. You don't want to slam the motor and battery by doing a hard jump off a curb especially on a bike with no suspension. Hard on the body and you really have to keep your eyes open and watch for oncoming or turning traffic if you're not stopping at that curb.
Mostly, get out there and have fun, Martinet and tell us where you go. A pic of you and the bike uploaded here would be cool too.