I've found that generally with houseplants when the leaves turn yellow the plant is usually rootbound or it's the natural shedding of older leaves. When they turn brown without yellowing first it's from overwatering.
Peace lily likes to dry out before being watered. The top inch or two should be dry before watering. You can stick your finger into the soil up to your first or second knuckle. Water until the water flows through the drain holes. Don't let them sit in water for more then an hour. Once the spathe (flower) has finished it's bloom it can be cut off. Browning or yellowing leaves should also be cut off close to the base. Your lighting is just fine.
#1. Once the plant has finished flowering it may not flower again for several months depending on the age, light conditions, watering and fertilizing. Transplanting will often cause a plant to shed it's flowers so it can concentrate on growing new roots.
#2. Yes, cut off the spade. Don't try and pull it as they tend to hang on until very brown and crispy.
#3. It appears that the pots are too small for the rootballs. Putting more soil on top of the roots is not a good idea. There should be at least one inch of space in the pot above the soil so that when you water, the water doesn't run over the top of the pot. When I water I usually just fill up that inch with the water and I'm done.
#4. I have several plants in one pot and it looks full and lush. It's easier for me to take care of larger pots as I often forget to water. The smaller the pot the more often you need to water. The more sun the quicker the soil dries out and the more often you will need to water. The more rootbound the plant in it's pot the more often you will need to water. I have two different varieties of peace lily, one with very large leaves that aren't shiny and another with smaller leaves that are shiny. My plants will often wilt completely and droop before I remember to water them. Peace lily doesn't mind this and will thrive better that way then if they are overwatered. If you are going to put them all in one pot, unpot them and GENTLY shake off a bit of any loose soil so you can group them together and see what size pot you will need. Since you are in a foreign county it might be best to measure the circumference of the group with a string and purchase a pot that is about 2" larger then the combined rootballs. Just stand the plants up without their pots and any extra soil snuggled in a group and measure. Take your marked string with the 2" added with you to the store. The next time you need to repot after this, use a pot that is 2" larger. I suspect that won't be for another year. Btw. mine don't get any extra humidity then what is in my house and they've been very happy for 15 years now.
Here's some sites that have some great tips on how to pot and grow your plants.
For your lovely galvanized planter consider some succulent plants that stay small and don't need alot of water and attention. Most will thrive with only 2 to 4 hours of direct sun. There are many different types of aloe and aloe looking plants. Some aloes will get huge (aloe vera) and others stay small. Here's some ideas, including the smaller aloes, though I don't know what you'll find in Budapest! This site says that plants need low, medium or high light. Medium would be a bright spot like your peace lily. This first one comes in a very tall variety often called 'Mother in laws tongue' or snake plant. This rosette one that I have sits away from all windows. Once in a while I'll put it near a window if it starts to 'stretch'. I usually remember to water it when it's as dry as the Sahara!
These peperomia come with lots of different colored leaves and stay small. They have the weirdist looking flower stalks. Just one of each color in those little galvanized pots would look lovely. You can see there's lots to choose from.
Here's the main page where all of those pictures came from. You can browse by the photos, the common name or the scientific name. You can search too.
Don't feel badly about asking questions here. I know what it's like to be in a foreign country and not speak the language. I spent 4 months in Peru and didn't speak more then a handful of Spanish. When I went into a little grocery and managed to make enough chicken noises so that the lady knew what I wanted, she brought me a live one!!! Life sure is different in other parts of the world.