What is the difference in use between 以及 and 还有
I think the primary difference is formality.

以及 sounds formal. It is rarely used in spoken language but acceptable, okay in casual writing and common in formal writing.

还有 sounds very colloquial. It's fine in casual writing but should be avoided in formal writing.

It's not true to say 以及 only connects phrases. A quick search will give you many good counter-examples. However when it comes to connecting phrases, 以及 does a better job than the other choices. That's exactly where people would use it in colloquial language - connecting short words with 以及 sounds too formal but connecting long words or phrases sounds okay.