3. Yes, it will get easier. You'll get better at using the downhill portion to propel you back up the next hill. Use your lowest gear! That's what it's there for. The easiest way to bike uphill is to ride in a low gear at a high rpm. It saves your legs for the next hill. Don't grind away slowly at a higher gear.
I have a kiddy bike that I bought off Kijiji for $12.50. I don't think it has gears...
My neice's bike has gears, do you change it as you go? kind of like a standard car?
Well, there's your problem. This is what's called a 'fixed gear bike'. Many children's bicycles don't bother with gears, because the manufacturers assume that they will only be riding in a small area that will be mostly flat. Secondly, it may be that the bicycle is too small for you. An improperly sized bicycle will suck up all your energy, instead of converting it properly to power to get you up those hills!
Here is a pretty good explanation of basic sizing:
http://www.gobiking.ca/bike-fit/index.htmlBut yes, gear on a bicycle are pretty much exactly like in a car, except there's no such thing as a clutch. They are usually controlled by toggles, with 1 toggle meaning 'shift up a gear' and 1 toggle meaning 'shift down a gear'. Sometimes they are controlled other ways, for example, by rotating the handlebar kind of like on a motorcycle. Low gears are for climbing up steep hills. High gears are for if you want to be able to add more speed when traveling downhill. Flatter parts of the world sell more bikes with no gears or older style gearhubs with only 3-5 options. Hillier parts tend to have more options with more gears - I ride an 18-gear (3 front, 6 back) and a 21-gear (3 front, 7 back). More gears can make it easier to get up and down hills of different slopes, as you can fine tune to match the difficulty.
If nothing else, get a bike that is the right size. Then think about gears/no gears. Then think about riding style.
A more upright posture will be more comfortable on your back and put less pressure on your groin, but will reduce your power while pedaling, meaning slower speed and more difficulty on hills. Here is an example of a rider on a 'cruiser' bike, see how her torso is almost completely vertical, while she is able to comfortably hold the handlebars and pedal?
http://www.freeenergystore.com/BCFull2.JPGAn intermediate posture will be a mixture between comfort and efficiency, most mountain bikes and what are called commuter or 'hybrid' (because they are hybrid between road and mountain styles) bikes will offer this kind of posture. The back will be leaning forward, somewhere around 45 degrees. This is a typical 'hybrid' style:
http://bustedknucklebikes.com/wp-content/uploads/shutterstock_1574132661-450x299.jpgSome commuters like what are called road bikes. These focus on speed. They have narrow tires that are fast on paved surfaces, but poor on dirt or gravel and more vulnerable to flats. They often have 'drop' handlebars, to allow an even lower torso and more efficient pedaling. These are very powerful to climbing hills, but if not fitted properly, can be tough on the wrists, back, and groin. An example:
http://cdn2.coresites.mpora.com/twc/wp-content/uploads/2013/04/ruby6.jpegI hope this little primer will help you figure out what to do. Rain can be overcome! Hills can be overcome! Having the right tools helps.
Here's photos of people being drenched in water (I've been there) :)
https://www.flickr.com/photos/bikeportland/sets/72157636056592224/