Q. Paulowia tree and sap problem?
The mystery plant may be the Paulownia tomentosa, common names Foxglove Tree, Princess tree, Empress Tree, Royal Paulownia native to China. It does have large heart shaped leaves, and pretty flowers, although the color is described more lavender pink. Here is a picture of a full-grown tree, which loses leaves in the winter (deciduous) http://www.pfaf.org/user/Plant.aspx?LatinName=Paulownia+tomentosa . Some people like the look of these trees, although some species are very invasive pushing out native trees, but some are not invasive according to one link I found; Paulownia Elongata suppostively may not be invasive, and P. tomentosa may not be invasive in every state. Well, it’s difficult without the flower to positively identify your specimen.
Picture: https://www.nps.gov/plants/alien/fact/pato1.htm It would be a dead giveaway if you had a picture of the flowers.
Sap problem may not be the tree but an insect secretion: https://www.extension.umn.edu/garden/yard-garden/trees-shrubs/removing-sap-and-honeydew-from-cars/
Hope this helps.