と and や are used to connect two or more nouns.
Most of the time, と can only be used for a fixed number of items like:
"キーボードとマウスいる".
(we need) keyboard and mouse
But や is used when there is a variable/unknown length like:
"キーボードやマウス、そしてLANケーブルとかいるかも"
(we need) keyboard, mouse and probably LAN cables also.
Also や has some sense for "OR" or "AND/OR" in
「日本で寿司や刺身を食べたことがまだありません」
I haven't tried Sushi and/or Sashimi in Japan yet.
But と only means "AND"
「日本で寿司と刺身を食べたことがまだありません」
I haven't tried Sushi and Sashimi in Japan yet.
そして is used as a conjuntion between two phrases and has the sense of meaning "then ..."
~たり is used to connect two verbs and is used in the sense of giving examples, like Lukman mentioned in the comments:
泣いたり笑ったりのは生きてるものさ
~くて is used to connect to adjectives like:
彼女は美しくて、格好いい
She is pretty and has wonderful style
And yes, ~し~し is used to connect two adjectives, with exclusive positive or negative senses:
この部屋は綺麗だし広いし間取りもいいから人気がある。
This room is clean, wide and also good partition, so most of the people like it.
あの部屋は汚いし暗いし駅からも遠いからなかなか借り手が見つかりません。
That room is (a bit) dirty, (kind of) dark, and far from the station, so nobody bothers to rent it.
Normal usage of ~も is too / also, but there is some usage as "AND"
これもそれもあれも全部欲しいな
I like to have this, that and also that one, basically all.
And there are some more forms like ~かつ~ (plus .... or not only ... but also ...)
必要かつ十分
requirements and fulfill
and also 及びに、並びに、ともに、おまけに have a similar usage to "AND"