Lychee tree in Vancouver?

Went to the Harbour Green Park during lunch time to get a breath of fresh air. In this park, there are these trees giving fruits of beautiful colors. These fruits look like lychee, a tropical fruit native to Asia. Therefore, I am not too sure if this is a correct identification or it's a modified species here in North America. Nevertheless, it is a beautiful bright fruit in such a gray season so far.

And these are its flowers.

On the trees, I also saw these invertebrates crawling (vertically) along the bark of the tree, so I definitely don't think they are worms.

Nearby, I came across this beautiful spider. Another unable-to-identify challenge, oh joy!

Not such a great day (season) to overwork the brain, but at least I got outside and took these pictures (actually, it took me more than 30 to 40 pictures just to get this half-decent picture of a spider). Terrible.
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