Well, unfortunately it seems that one cannot place custom markers and draw (and obtain coordinates) directly from maps.google.com if one is anonymous/not logged in (as it was possible some years ago, if I recall correctly). Still, thanks to the answers here, I managed to make a combination of examples that has both the Google Places search, and allows drawing via the drawing library, and dumps coordinates upon making a selection of any type of shape (including coordinates for polygon) that can be copypasted; the code is here:
This is how it looks like:
(The Places markers are handled separately, and can be deleted via the DEL "button" by the search input form element; "curpos" shows the current center [position] and zoom level of the map viewport).