Question 2 The statue is hollow but sealed on the bottom. Here's a topologically equivalent version:
Question 3 Ignore the shape labeled "S". The other two shapes (labeled "S'") are topologically equivalent.
Question 5 (It's not a ribbon -- it's a kind of hollow triangular tube, kind of like a long, curved prism)
Question 6 Your surface is the last one; the pictures illustrate that it's the result of glueing two pairs of pants together, just like I did two T-shirts in class.
Question 7 A hollow dodecahedron
Question 10 THis is made of varnished paper; it is a kind of squarish tube (i.e. a short section of this shape resembles a cylinder whose cross-section is a square instead of a circle).
Question 11 All three of these are topologically equivalent to each other. Note that there are no boundaries: you can see in the first picture that what might look like an edge in the green pictures is actually just a fold in the paper.
Question 12 Please disregard all the crinkly features of the surface; it's just supposed to be a computer geek's Christmas wreath!
Question 13 The left and right sides are supposed to be glued into separate little shapes as we have done before; each is then a surface without any boundaries except the little circles in the middles. Then the two little shapes are glued together by identifying those two circles.
Question 14 small statuette produced by a 3D printer.
Question 17 You can ignore the red and green stuff -- but do you see that there's an interesting game to play here?
Question 18 3D printer version of a classical statue of two kissing children. Notice the space under their chins.
Question 20 It's a coffee mug -- isn't it? ...
Finally, here are some other illustrations I found online which I present just for your amusement.