Can GERD worsen dysphagia?

Yes. Gerd can cause peptic strictures (narrowing) of the esophagus as well as reflux-induced esophageal dysmotility (abnormal peristalsis / contractions).
Yes. Gerd or reflux from the stomach back into the esophagus can cause changes in the lining of the esophagus. Those changes make it difficult to pass food and can also be a kind of 'pre-cancer'. If you have gerd, you should have a GI or ENT doctor who is periodically looking at the esophagus to ensure that there's no danger.