Application forms are strict about photographs: an exact width and height, sometimes an exact file size, and they reject anything that misses. Here is how to hit the numbers exactly.
These are three separate requirements and people usually try to solve them at once, which is why it goes wrong. Cropping decides the proportions. Resizing decides the pixel count. Compression decides the file size. Do them in that order and each step stays simple.
Do not force a width and a height that do not match your photo's proportions, or the picture will stretch and faces will look wrong. Crop to the right shape first and the resize becomes a straight scale with nothing distorted.
One limit worth knowing: enlarging a small photo cannot invent detail that was never captured. If the form wants 600 by 600 and your original is 200 pixels wide, the result will look soft no matter which tool you use.
35 by 45 millimetres is the most common print size, and forms often ask for 600 by 600 pixels or similar. Use the number on the form you are filling in, not a general rule.
No. You are keeping fewer of the original pixels, not rebuilding them. It is enlarging that costs quality.
No. Every step runs on your own device.