This could be a loooooong answer becouse you have a lot of confusion.
I have a question what that nobody seems to know the answer to.
There is no mistery here. The standard resolutions is something most people on the business know. Remember, to find a good answer you need to know what to ask.
I have to make small stickers with ingredients lists (100mmx50mm), i know i should use illustrator but all i have is photoshop.
You can download Scribus for this that is free. I thought the images were huge. But later I figured out what you ment.
The Printing company told me that they were unable to print my stickers (300ppi) because when they zoomed in 1200% or more, the images got pixelated, and that was why one order of stickers had "hairy" letters.
Ok, so you did NOT make them at 300ppi on photoshop? If you make a document 10x5cm at 300 ppi you dont need to upscale anithing at 1200%.
I was suprised because it seems like a weird issue, so i started to increase the dpi of the images, so they would look better in 1200% zoom (and why would you have to zoom in that much as the sticker is so small itself).
It is not a wierd issue. You do not need to "zoom" it, you need to make them at the necesarry resolution from start. That is why you need to make them in vectors, They are scalable, raster is not.
So i made a design for a magazine, afterwards they told me that they did't want the pdf file but jpg file of the design
Stickers or magazine? Ok. You are mentioning previous experiences. Yes, sometimes is safer for magazines to handle a good quality jpg.
when i compressed the picture and saved it had a bad quality so i increased the resolution to 500, they called me back and told me that 300 is the maximum for printing.
If it had bad quality it is not corrected increasing resolution to an unnecesary value.
Bad quality can be maaaaaaaaany factors. Bad original photo, too much compression, bad color space, bad ink amount.
I have read about this but can't find an answer on how to resolve this issue, okay, magazines are max 300 but what about the stickers? Is 300 ppi max for printing or can files with bigger ppi also be printed (let's say 1000ppi)?
Ok here is the real issue.
1) A raster image is normally printed (on comercial offset) at 150 lpi which is a diferent unit, but the file as a standard should be delivered at double that. 300 ppi.
But a vector font is printed at the maximum resolution the printer has set for that project. For 150 lpi the printer is set normally at 2400dpi.
The least you want is 600 or 1200 dpi. Notice. ppi on a raster image, 1200 dpi on a vector shape. Fonts in this case.
Use google translator for this complete explanation http://www.forosdelweb.com/f6/hablemos-resolucion-697586/index2.html but as a summary:
A) A printer uses its dots (dpi) to form a line (lpi), to reproduce the gray values contained on a pixel (ppi).
A font it is not converted into a LPI it is printed directly.
What I meant by making the stickers, was that i have to create them with photoshop,
No, you do not have. Prepare your background on Photoshop with the correct resolution and phisical size. 10x5cm at 300 ppi.
Add small fonts on Scribus that is free. http://www.scribus.net/
Deliver a well prepared pdf which contains raster and vectors.
Note: I think you can actually export fonts as a vector inside Photoshop to a pdf. I am too square for that becouse I necer do that. Probably someone can comment thoose steps.
I am talking about stickers containing the ingredients list behind on product packages, black and white. Very small size and font, but still readable.
If the font is not that small you could make it in photoshop. It is not the best case senario but you could get away with it.
It does not matter if it is a sticker or a magazine. The factors that define the resolution of a file are:
Substrate. Coated paper or Uncoated paper, Newspaper, Cloth, Vinyl, etc.
Printing technique. Sheeted offset, Silk printing, Flexography, Rotary offset, High Ouality book art print, etc.
Rasterized cmyk or monochromathic 1bit image. A normal photo could be 300 ppi while a manga type cartoon or a font could be 1200ppi.