You've already received excellent advice, so I'll just describe a few things we've been doing for years. Our bird baths are a distance from the house, so in addition to those, we provide water on the patio just outside the door, as you're planning to do on your balcony and terrace.
For drinking, we put out shallow saucers. A convenient choice is the saucer a potted plant sits on. Some are plastic, others are ceramic, and some are just heavy-duty paper plates from the supermarket. We use a lot because, although the small birds share well, the larger types seem to prefer their own. Chipmunks and squirrels enjoy them too. (If you haven't had a close-up view of a chip or squirrel sucking up water while holding the dish with their tiny feet, you've missed something awesome! Of course, I don't know if you even have those where you live!)
For bathing, a favorite of our birds is a plastic tray I use to start seedlings. It's a few inches deep; enough for the small birds to drink and bathe but not deep enough to drown. Anything like that would work. My picture on the left was taken during birdy play-time! I apologize that it's messy, but if you press on it, you'll get a larger view of them. It's too bad I don't have a video; they make a fun splashing sound! We also have a plastic bird feeder with a dome above it. It doesn't work for bathing, but the birds drink from it, and it offers a little bit of protection from the weather. It's the one from which the cardinal is eating in my picture below.
In the United States, we have the opposite problem of those who deal with evaporation. During the cold winter months, our water quickly becomes little blocks of ice. Every day, sometimes twice, we dump those out and refill the dishes with warm water. Rather than bringing in all my containers, I fill up a watering can, or any pitcher I have lying around, step outside and tend to them all at once. It's quick and easy! My caution for those in colder climates is that glass dishes tend to crack in the winter, leaving jagged edges which aren't safe for the birds. Plastic can crack too, but doesn't usually break apart.
Whether it's too hot or too cold, there are times when birds rely on us for their survival, and I applaud your desire to help them!