Hi and welcome! Glad you're here.
You might want to check inside your cabinets, under the countertop. Most are attached that way, and if you unscrew them you can lift them right off. Of course, break the seal at the wall first, and disconnect the sink plumbing.
The tile on the wall would be easiest to remove with a prybar, sledge or if its on drywall, just cut it out, drywall and all.
As for the jointing of the countertop, I will leave that to the Installation Department...aka Tigratrus and Torrus.
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