There appears to be a partial eclipse of Venus when you use the backyard telescope. Is this a normal event, or is it connected to the transit-of-Venus expected in June?

No, no no! There cannot be an eclipse of Venus, because no dark object is close enough to it to block its light, or shade it from the Sun.

What you are seeing are the phases of Venus, similar to those of the Moon. Like the Moon, Venus shines in reflected sunlight, but unlike the Moon, we never see all of its sunlit face (it would have to be exactly on the opposite side of the Sun). Usually we see part of the sunlit part--often just a thin crescent--and part of the dark one. What you saw through your telescope was also seen by Galileo (1609 or so) with the first-ever astronomical telescopes, and once he understood it, he realized Venus must be a planet orbiting the Sun, strong evidence that Copernicus was right.

The transit of Venus occurs when the planet comes between us and the Sun, when it appears to be a dark spot crawling across the Sun's disk.
At that time, in a little over two months, Venus will present to us only its dark side. As it is now approaching that position, the side we now see is mostly dark and it appears as a crescent.

This week's question is provided by Dr. David Stern. Dr. Stern is a physicist retired from GSFC, who has created several large web-collection on astronomy, physics, space and magnetism. This question is one of many received from users of his site.