Firstly, I am not sure when you last played, but this aspect of Simutrans-Extended has not changed significantly in some time - since before the name change from "Experimental". Street level transfers, as you term them, still work in the way that you recall.
The idea of the coverage area being large is this: a person can in principle walk quite far, and will do so if there is no other means of getting to where he/she needs to go. So, for example, in a medium sized town in 1850 with only a single railway station, people living on the periphery of the town may walk several kilometers from the periphery of the town to get to the station. 'Buses were rare in the 1850s (and in any event were only affordable by the middle classes), so this would be what one might expect.
However, all passengers have a journey time tolerance. This tolerance is different for each passenger generated. Walking, including walking from the passenger's starting point to the first stop, walking between stops, transferring within a stop, and walking from the final stop to the destination building, all takes time (on the basis of a speed of 4km/h travelling in a straight line). This time is taken into account when computing whether a journey falls within a passenger's journey time tolerance.
For example, suppose that, in the town in 1850 with a single railway station, a passenger wishes to travel to a building in a neighbouring town served by that railway. The passenger's journey time tolerance for the one way trip is 1 hour and 30 minutes. The train takes 30 minutes to complete its journey, and there is an average of 15 minutes waiting between each train. The station's internal transfer time is 2 minutes. Taking out of account walking, this would give a total time of 47 minutes - well within the passenger's journey time tolerance. However, suppose that the walk from the passenger's origin building to the railway station were 45 minutes, and the walking time from the station at the other end of the line to the passenger's ultimate destination were another 15 minutes. This would give: 45+2+15+30+15=107, or 1 hour and 47 minutes - in excess of the journey time tolerance. The passenger in that instance would not travel (assuming no accessible alternative destinations).
Similarly, passengers who are able to get to their destinations in multiple ways will always choose the journey with the lowest overall time. Again, this includes walking times and internal station transfer times. This might mean that a trip by 'bus which is nearly door to door will be preferred over a trip by a faster train where the better speed of the train is outweighed by increased walking times between origin and station, and station and destination.
This means that there are many situations in which it is beneficial to build stops within the coverage area of other stops: passengers will choose a starting stop based on whichever overall journey time will be the lowest.
As to the internal transfer times of stations, you can see this in the station details window. This is determined by the area of stations, and represents the time that it takes passengers to walk within the stations. This can be increased if the station is overcrowded. This does mean that there are situations in which it is better t have several neighbouring stations rather than a single, large integrated station. (For example, an airport can be split into multiple terminals, all sharing the same runways, each a separate stop).
To answer your final question, intermodal transfers are handled in exactly the same way as intramodal transfers.
I hope that this assists.