I will have an 11 hours flight and I would like to have suggestions on how to make it through as smoothly as possible. I don't want to eat the vegan food served. I have never asked if I can bring fruits on the plane, but that's not possible, right?

In the taxfree they usually only have unripe bananas and apples. I don't like that. I found myself in the past wanting to drink lots of water on these flights. Shall I fast?

Hey Robin!
Where are you flying from, and to where?
They may allow you to bring your own fruit. Usually, the regulations insist that you cannot land with your fruit and take it through customs. But, it depends on the country you are travelling to.

From Sweden to Thailand.

Great! Are you having a holiday there, Robin?
You can take some fruit with you as a carry-on item. A bag of fresh fruit that you intend to polish off before landing counts as "one carry-on item". I believe you are allowed to carry another bag or personal item along with this.
If a bag may leave too much opportunity open for the contents to get mushed (such as many ripe fruits would do in a plastic, paper or cotton bag, you could take your food in a small box. When I fly, people take on board boxes of donuts that consist of several layers on wide trays. I sometimes take on board a box of similar size, loaded with fresh fruits and vegetables to make the journey an enjoyable one.
11 hours is a long time in the one spot. I suggest getting an aisle seat to free you up to move about and get additional water when you need to. It's important to be peeing clearly while you are on such a long flight. If you aren't peeing clearly, or if you simply don't pee at all for more than two or three hours, then you are becoming dehydrated. Taking on board veggies like celery and cucumbers can replenish your need for water without giving you as many calories as fresh fruit would. Because you are in an airplane, you would probably be fairly inactive for that period of time. I doubt you would need to consume a large amount of fruit while you are up in the air. It would be more critical to stay well-hydrated. The dry air of the plane cabin sucks your body's moisture from you more rapidly than you may expect it to.

No, I was wrong. Even in the tourist class it was possible. However, only with help of agency.
I mixed it up... after I had bought the ticket, when I logged in the internet site of EvaAir, I could do check-in and some other things but I was not able to change the diet (only the VIP, business etc. classes could do it this way). Then I just emailed the agency and they managed it easily, we had the meal we wanted.

Have a nice time in Thailand.

Thank you very much. I will be investigating the possibility of bringing my own sweet fruit. And by the way, exercise or not, I can eat so much fruit and it appears like my weight stays were it is.