そして details

Examples

and then — the next thing that happened, in narrative order

昨日きのうは友達ともだちとご飯はん食たべたんだ。そして、カラオケに行いったよ。

kinou wa tomodachi to gohan tabeta n da. soshite, karaoke ni itta yo.

I had dinner with friends yesterday. And then we went to karaoke. casual

彼かれは大学だいがくで経済けいざいを学まなんだ。そして、卒業後そつぎょうごは銀行ぎんこうに入はいった。

kare wa daigaku de keizai o mananda. soshite, sotsugyougo wa ginkou ni haitta.

He studied economics at university. And after graduating he joined a bank. neutral

and — adds one more fact to what was just stated, with no order implied

この店みせは値段ねだんが安やすいです。そして、味あじもいいです。

kono mise wa nedan ga yasui desu. soshite, aji mo ii desu.

This place is cheap. And the food is good, too. neutral

弊社へいしゃは品質ひんしつを第一だいいちに考かんがえております。そして、その姿勢しせいは創業そうぎょう以来いらい変かわっておりません。

heisha wa hinshitsu o daiichi ni kangaete orimasu. soshite, sono shisei wa sougyou irai kawatte orimasen.

We put quality first. And that stance has not changed since our founding. formal

それから
そして only claims the next thing belongs with the last one, so between two clauses it links states as readily as events (安やすい。そして、うまい); それから between two CLAUSES recruits temporal order, so forcing it between two simultaneous facts asserts a sequence that isn't there — order-free それから survives only in item lists (コーヒー、それからケーキ).
て
The て-form is a MORPHEME welded onto the verb — it chains clauses inside one sentence and leaves tense to the final verb, so it can never open a sentence; そして is a free word standing before the clause, which is why it starts a new sentence where て only extends one.
それに
そして only claims the next thing belongs with the last, so it will link two events in sequence (東京とうきょうに行いった。そして、大阪おおさかにも寄よった); それに adds a further GROUND pulling the same way as the last point, so it misfires on a bare sequence, and 安やすい。それに、まずい fails outright because the second point pulls the other way.