Yes. It takes a fair amount of practice, but can be done simply by starting to do more with your off hand. Start with simpler tasks. For instance, don't start with shaving or applying makeup. Start with simple tasks and work up to more complex tasks. As with most skills, the more you practice, the more quickly you will progress.

I would like to become ambidextrous ! When I'm learning my lessons and stuff I write with my left hand. To start with it's quite neat but afterwards I get tired...

I worked at it in high school because I thought it was so cool. It took a LOT of practice but it was WORTH it! I'm only a little ambidextrous but it does enrich facilitation throughout life. I may do all kinds of odds & ends with my left that I otherwise would reserve for my right. If I do a lot of writing I might switch to my left but that's still hard to do. I receommend doing various tasks with your odd hand until you get better at it, but it does take a very long time to get really good at it.

Yep, I think so. My sister broke her right arm so many times she had to learn to write with her left; she writes equally well with both hands now.

Well, in short, yes. It's said that certain people are born with the ability to write with both hands, use both feet whilst playing football etc. It's not impossible to teach yourself to be the same. It just takes a lot of practice and time. It can take up to a few months for quicker learners that are pateint enough to train themselves, yet anything up to a few years for those that practice less. Generally, as with most other skills, the younger you learn at, the quicker you are likely to pick it up. To be fair, I'm actually training myself to be amibidextrous, as I play the piano and struggle to use my left hand as fluidly as my right. There are a few little tricks you can use to begin training yourself and getting your brain to accept that it won't be subconsciously using your dominant side for most activities. For starters, try using your computer mouse with your opposite hand, and when you type, try to make your opposite hand be the dominant 'typing hand'. (I'm actually doing that right now). Try writing "the quick brown fox jumped over the lazy dog" (a sentace with every letter of the alphabet in it) a few times every day. You'll see your handwriting get progressively neater the more you practice. Arguably, some think there are better things to do with your time, but there is only so much forced concentration in High School that I can take. So in answer to your question, it's possible, though you have to be patient with yourself. Good luck to anybody that is trying to train themselves to use this skill.