- My plan is to start creating my time-lapses in 4K format. From there I have figured out that my pictures need to be at least 3840 × 2160 pixels which means that every camera above 9 mega pixels should work fine. Is this theory of mine correct or my calculations are totally wrong?
It's more complicated than that. 3840 x 2160 has an aspect ratio of 16:9. Most DSLRs shoot a 3:2 aspect ratio. So 8 MP would be ~3464 x ~2310 for most DSLRs, which won't quite get you the width you need. You might want to go with at least 10 MP, which gets you ~3888 x ~2588
- During my research on the internet I noticed that many people are comparing DSLR against Mirrorless cameras. Could someone please explain what the difference is and which one is better for time-lapses. (Will the quality significantly decrease if I use a basic camera?)
This is really a separate question. I recommend reading this question for more info.
- I know that this is more or less personal preference but is there a standard for how many pictures per second the camera needs to take so that the time-lapse to be in a very high quality.
What are you going to be taking pictures of? This can make a big difference. If you're shooting stars, you're limited by the need to take long exposures. You'll likely want to use a 15-30 second exposure, which limits you to at most 4 pictures per minute. But if you're shooting in the middle of the day, you might be able to shoot at 1/8000th of a second, which is a lot more photos per minute. If you really want to shoot more than 1 per second, you might want to go with video instead.
- From the information I have found, I realized that taking a picture per second is far better than just recording a video and then speeding it up. Do you agree with that?
It depends on the situation and the artistic effect you want to create. Having it as video allows you to change some parameters and experiment after-the-fact. But it requires a lot more memory to store so many images, especially at high resolutions. I would recommend starting with just still photos. Video retiming is really cool and fun, but requires a lot more work.
- Is this the right formula to calculate how many pictures I need for an X seconds of video ----> wanted video duration * 30 frames per second = total pictures needed?
That's a reasonable way to do it. You don't have to limit your resulting movie to 30 fps. If your desired output device is a computer screen or modern TV, you can just as easily choose 24, 25, 50, or 60 fps. I personally like the look of 24 frames per second video, especially if I'm trying to create something otherworldly like a time lapse.
- Will there be a significant difference for time-lapsing if the video is in 30 or 60 frames? After all our eyes can see 24(ish) frames per second.
"significant difference" in what? Certainly you'll use a lot less memory and bandwidth at 24 fps than at 60 (assuming the same quality per frame). They will look different, also. Whether your audience will appreciate the difference is hard to say. I work in the professional video space and have colleagues whose home televisions are set to change everything into 120 fps and gives everything the quality of having been filmed on a cheap video camera. If they can't tell the difference, most other people certainly won't. But I definitely notice it.
- I know that camera gears are usually very expensive. Could you please recommend to me the cheapest camera which you think will do the job. (As I mentioned above, this will be a hobby, I am not planning to do it for a beneficial gain.)
You'll likely be fine with any recent model from any major manufacturer. I've had good luck with Canons. A used Canon Rebel will cost you in the mid hundreds of dollars and should do fine. If you prefer Nikon, they have equivalent models, as do Sony, and most other manufacturers. You can find an intervalometer (a device which continually triggers the camera at an interval you set) for very cheap on Amazon. I think I got mine for $25 in the last year. You should get a reasonable and appropriate lens for whatever you're shooting. Without more info, we can't give you recommendations. (We don't know if you need wide angle, telephoto etc.)
Clarification: There seems to be some confusion in the comments, so let me clarify something. Any camera can be used for a time lapse. All you need is a way to trigger it periodically and enough memory or film to store the images you're taking. I have personally made time lapses with my now 10-year old Canon Rebel xTi, so I know for a fact that it is possible. Some cameras have a built-in intervalometer, while others require the external unit. For example, here's one that works with Canon Rebels.