I've noticed that in a rural area with low pollution the relative humidity is constantly lower than the humidity in a high polluted city. Is there any correlation between pollution and humidity?
By way of reference, "humidity depends on water vaporization and condensation, which, in turn, mainly depends on temperature".
From the information you have supplied in your comments. There are waters in Bucharest and forests in the suburbs, but no waters or forests where the country house is located.
From your information, Bucharest has a number of sources of atmospheric water vapour, the river that flows through it (evaporation of water) and the forests in the suburbs (transpiration of water). Additionally, motor vehicle exhausts will increase the humidity as water vapour is one of the products of the combustion of hydrocarbons.
The warmer the air, the greater its capacity to hold moisture. Cities tend to be warmer than rural areas due to the heat island effect, which is the result of modifying land surfaces and the generation of waste heat.
Humidity in the rural location will arise from evaporation of water in the soil and transpiration from crops or grasses. Such transpiration will produce less water vapour than forests. Additionally, the rural location will have significantly fewer cars producing water vapour in their exhausts. Consequently, the rural location will be less humid than the city.
The reason why Bucharest is more humid that the rural location has more to do with the greater availability and vaporization of water in Bucharest and the temperature of Bucharest than the amount of pollution in Bucharest.
Relative humidity, while a nice way to gauge how air might feel (comfort), is a poor measure for comparison between different times during the day. Of note you observe:
Every morning we have a 90-100% relative humidity here (in the city) and decreases to 60-80% later in the day.
This is merely an effect of the diurnal temperature change. Relative humidity is the ratio of the actual amount of water vapor in the air compared to the amount of water vapor needed to saturate the air. The water vapor needed to saturate the air is a function of temperature. Warm air needs more water vapor to be saturated than cold air.
If you have air with a constant mass of water vapor and vary the temperature between cold (e.g. 7 AM) and warm (e.g. the afternoon) you will have the same pattern of relative humidity you have observed -- very high in the morning and decreasing during the day. This is a normal pattern and absent of any effects moistening or drying the air you will observe this daily pattern of relative humidity in many places.
Right now for example at 7:30Am, in Bucharest the temperature is 2C and relative humidity 93%. At the country house (90 km away), the temperature is 0C and 45% relative humidity.
Air at 2 C and 93% RH has a vapor pressure around 6.5 hPa and air at 0 C and 45% RH has a vapor pressure around 2.8 hPa. This means the air in Bucuresti has a little more than twice the water content of the air from your rural location. The other answer by Fred gives some good reasons how this can arise.
A few other reasons can be the large scale wind motions and where your rural location happens to be. Bucuresti can often be in westerly winds where some moistening occurs from flow over the Danube and further moistening within Bucuresti from rivers and lakes. As Fred noted, urban areas tend to be warmer than rural areas so there is more capacity to hold water vapor (before saturation is reached).
You don't mention where your rural home is, but if it happens to be to the north or north west (e.g. Ploiesti, Pitesti, Buzau) then you have orographic effects from the Carpathian mountains that can dry out the air. If flow is up and over the mountains then the air is cooled as it flows upslope (on the Transylvanian side) where it becomes cloudy and can precipitate. This reduces the amount of water vapor in the air and as it flows downslope and warms it remains dryer. I could give a more specific large scale flow explanation given the location of the rural house.