In busy areas such as train stations, metro stations, football stadiums in Ukraine you will see toilet facilities that look like this (even in the ladies toilets). Regular toilets will be found in hotels and restaurants. In the busy areas and when entering a toilet using the toilet is generally free of charge, you may need to purchase toilet paper which costs roughly 2 Hryvnia. Toilet paper is purchased from a lady who will usually sit at a small desk as you walk in to the bathroom. There are usually good facilities for hand washing and drying.
Ukrainian Orthodox is the main religion within Ukraine and indeed in Ivano-Frankivsk. When driving around the country you will see many grand churches in even the tiniest and poorest of villages. Due to the large Jewish community you may also see Synagogues. You will notice Orthodox churches straight away as they have the Russian style Onion shaped domes.
Along long rural roads and in villages in Ivano-Frankivsk you will notice many "shrines" that will just be placed in the middle of nowhere, they will have statues and photographs of Mary and Jesus, sometimes decorated with flowers. These "shrines" are for travellers, if you are travelling a long journey and you need to pray you will pull over beside the shrines and enter and you can pray. Many of these shrines are built by local people, many will have their own in their front gardens. (see picture 3)
In my experience of Ivano-Frankivsk most of the population in this area speak Ukrainian. This may sound a rather obvious but many cities in Ukraine (in particular Eastern Ukraine) speak mainly Russian. The dialects in Ukraine tend to vary quite vastly and Ivano-Frankivsk is no exception. The dialect can almost sound Polish in some areas but you will still be understood if speaking in Ukrainian.
You will find when travelling around the rural areas of Ivano-Frankivsk that there will be many people stood beside the road trying to wave down your car. This happens often but more so on market days. From what I was told from my interpreter it is fairly safe but use your own caution and common sense before picking up random people on the streets. Personally it is not something I would do but each to their own!
This is a popular custom in the rural areas and there is no right or wrong answer for charging someone money towards your fuel, some people ask for money for fuel some people don't so it is completely up to you which you decide to do but make your intentions clear when you first approach the person rather than leaving it until you drop them off.