I have set up as on one of the screens, but the pump from mod just do not connect to ship
Can someone help me deal with it? What is wrong?

maybe you need to move the pump closer towards the ships. the mechanics recently changed due to a change in vanilla and the picture on here is actually outdated.
when placing the pump there should be green markers telling you where valid positions for pump placement are

Is there a specific place on the ship that the pump needs to go? I've only managed to get mine to connect twice.

well in general its super difficult to connect the pumps while driving the ship manually. (similar to fluid trains, which are better to maneuver though than the oil tankers).
so you need to build a "port" first where you want the ship to stop, then, after buiding the port valid positions along this port will be shown to you by green markers when you try to place the "ship loadin pump".
i realise this somewhat backwards, because normally you probably will place the oil rig first, than the pump and as a last step you place the port. and you might be in a position where after placing the port you need to replace the oil rig and pump, because the former setup doesnt work correctly.