Why HDOP in TinyGPS++ is less than 1?
HDOP can be less than 1 according to this article.. I am no expert in this area, but according to the article, the HDOP=1 limit is based on 4 satellites; visibility and use of more than 4 satellites can reduce HDOP below this limit. When you think on it, this makes sense.

GPS specifications limit the inherent accuracy of a position solution through timing errors and vagaries in rf propagation through our atmosphere. Imagine drawing a vector from a GPS satellite to your receiver. The length of that vector represents the distance from the satellite to your receiver, but we depend on signal timing to infer distance/vector magnitude. In other words, we can only measure distance as accurately as we can measure time. 

Now think about the accuracy of a position solution based on a single satellite. If we assume the receiver is confined to the surface of the earth (and the satellite is geostationary), the single vector of length L1 will intersect the surface of the earth forming a circle. Your position could be anywhere on that circle - which could be quite a large range of values!

Now imagine a 2nd satellite, a 2nd vector of length L2 tracing a second circle. Now your position is constrained to be those points where the two circles intersect - two points! With a third satellite, a 3rd vector of length L3, one of these two points will be eliminated. 

Now replace those sharp lines with bands or swaths of some width D. In this case, the intersection describes a polygon instead of a point. We know our position is within the polygon, but with only three satellites that is the best we can do. 

As you can see, adding more satellites will begin to "slice off" sections of the original polygon, making it progressively smaller. So: HDOP=1 represents the limit with 4 satellites; more satellites yield a smaller polygon, and smaller HDOP. 



While writing this, I found a video that does a far better job than my words at describing the position solution process with multiple satellites.

This video is quite good also!