Difference between mo and to

一人正月の餅も酒もありそして

In this poem Taneda Santoka uses も to link nouns. I thought と should be used to link nouns - what is the difference? Also そして should only be used once, before the final noun in the list, right? Finally, what does あり mean in this context?

I believe the whole poem is as follows:

一人正月の餅も酒もありてそして
　
ひとり焼く焼き餅ひとりでにふくれたる

Yes, when you link nouns you use と, like "A and B (that's it)."

も is often used as "..., too" in English, such as:
- 私は明日のパーティにいきますよ。ボブさんは？(I'm going to the party tomorrow. What about you, Bob?)
- 私も行きます。(I, too, am going.)

も can be used to list things (without limiting to just A and B), something like "I have (as many things such as) rice cake, and sake, (among others)" or to emphasize "I have (plenty, like) rice cake, sake, etc."

And this そして is just there to connect the two clauses, "and then", it does not have anything to do with the final noun.

What I see in the original is ありて, not あり. But either way, it is a form of the verb あります (or ある in its dictionary form), and is equivalent to あって or ある in the contemporary Japanese. The meaning is "I have (something)," or "there is/there are (something)."

"New Year by myself, I have rice cake, and sake, and
I grill rice cake by myself, it puffs by itself"

There is a bit of a word play; "by myself" and "by itself."