How to ventilate my tiny kitchen when pickling chiles or making hot sauce?!

you should be fine with just a nearby window open. Actually you would be fine either way, but you will be more comfortable with a window open.

If you can open a window in the kitchen, and another on the other side of the house/apartment it will be better. Windows facing the same wall all are affected by the same breezes, but if you have a window facing another direction open, you develop a cross current and get better airflow. You don't need a strong breeze, just a steady flow moving in and out.

The biggest odor problem will be the peppers cooking, and any vinegars. It can be strong, but will go away quickly enough. An open window should be enough. Just try a small batch at first and see what happens, or try sauteing some chili peppers.

Wear gloves when handling large amounts of peppers! If you cut up one or two, then that's fine. You can wash that off, but with a lot of them you will not get all the capsaicin off your hand. Then, three hours later you will rub your eye and it will burn like crazy.

If you use vinegar in a hot pan or boil it, don't put your head over it to look in, and don't breathe in when you pour it into a hot pan. It won't hurt you, but the smell will be strong, and it can be irritating like cutting onions.

Open the window - that should be enough. Those recipes say well ventilated because the peppers can make your eyes water and you might get a bit choked up if you don't have good ventilation or fresh air. Especially if you are heating up the peppers, they can get strong!

I think you're fine with what you've got, I make hot salsas all the time, I've also made jalapenos pickled myself and there's no problem. Good luck, I think you'll like the homemade pickled hot peppers way better than the canned.

wear rubber gloves while chopping pepper's because if the pepper's are hot they will burn you hands