Even though you're downloading the family tree from your own account, it uses graphics from that site (the font, the overall style of the box, maybe the color of the font, maybe the font itself is licensed, the little leaf, etc.). Usually that kind of site is picky about using its graphics, but not always.
I didn't give any instructions for applying new links. I assumed removing the link from the whole image might fix that. But I'll have another look.
Right, when the layer is locked, nothing in it can be selected. So you have to make a new layer for your new graphics.
Technically, it is possible to lock only the JPEG, and still be able to draw on top of it, in the same layer. But locking objects can be tricky when it comes time to unlock it -- because it can't be easily selected
You don't have to lock the object or the layer at all. It's just an easy way to avoid selecting the JPEG.
Oh, no wonder you're having so much trouble selecting the rectangles. They're essentially transparent! After you draw a rectangle, and without deselecting it, open Object menu > Fill and Stroke > Stroke Paint tab. Then click this button
That gives the stroke a solid color. If you want to adjust the width of the stroke (outline), go to the Stroke Style tab > Width.
(The stroke was set for Unset before. Sometimes newbies get into this trouble, because they are clicking the question mark button, trying to find help. But in this dialog, the question mark is only used for a couple of advanced things.)
Or if you'd rather give them a fill color, use the Fill tab of the same dialog. Or just click a color on the palette.
Also, be sure to left-click, to select the object, before you right-click to create the link. It's not absolutely necessary, but when an object is hard to select, it's a little insurance that you have the right object.
No hurry, take your time