Doing two actions at once with ながら, and habitual/ongoing actions with ています.
Two actions by one person at the same time: A-ながら B (B is the main action).
おんがくを ききながら、べんきょうします。
I study while listening to music.
ながら attaches to the ます-stem (聞きます→聞き). Both actions are done by the same person simultaneously; the second clause is the primary action.
ています also expresses a repeated, habitual action.
まいあさ ジョギングを しています。
I jog every morning.
Beyond the progressive and resulting-state uses, ています with a time word like 毎日/毎朝 marks a regular habit.
し joins clauses to pile up reasons or qualities: “it's A, and B (too), so…”.
すずきさんは ピアノも ひけるし、うたも うたえます。
Suzuki-san can play the piano, and can sing too.
このみせは やすいし、おいしいです。
This shop is cheap, and the food is good.
し attaches to the plain form (of verbs, い-adjectives, な-adjectives + だ, and nouns + だ) and lists reasons or qualities, implying there are several. The listed items often take も.
It often leads to a conclusion (…から / だから), and pairs with それに (moreover) to add one more: …し、…し、それに….
それで links two sentences: the first is the cause, the second the result — “and so…”.
きのうは ねつが ありました。それで、がっこうを やすみました。
I had a fever yesterday, and so I stayed home from school.
それで starts a new sentence and presents its natural consequence of the previous one. Unlike だから, それで is not used to give commands or invitations in the second clause.