LaForte pluie inten/Forte averse

averse = downpour (it owuld be more accurate)
If you want to use "pluie", a heavy rain is called "forte" or "battante"

Hier, la pluie est tombée [plus tôt. ?]

plutôt = rather
plus tôt = earlier
A comparative would bring the question "earlier than what"? "Earlier than usual"?

Je prends l’autobuvais à l’'école et de l’écolen bus et j'en reviens aussi.

"je prends l'autobus À l'école" means you take it "AT school" not "TO(wards) school"
Honestly the most natural way to put it would be "je vais à l'école et j'en reviens en bus"

Quand j’avaite marchéais vers l’arrêt de bus, la pluie aur[a commencé/avait commencé ?] de tomber.

When I was walking to the bus stop, the rain HAD STARTED to fall (the action had begun) => quand je MARCHAIS [...] la pluie AVAIT COMMENCÉ
If you meant "started to fall" => A COMMENCÉ à tomber
"aurait commencé" would indicate a possibility that failed to happen (conditional past)

J’étais m’inquiétéète, car j’aussie devrait marcher pour ramasss aussi aller récupérer ma petite sœur, et après ça onnous devrions marcher cher notrerentrer à la maison.

Either "je m'inquiétais" or "j'étais inquiète" (with "inquiet" being an adjective)

je devRais, nous devRions = I/we SHOULD (conditional present)
je devais, nous devions = we HAD TO (indicative imperfect)

There is never any adverb between a prounoun and its verb in a simple tense => je devais aussi

"aller" would be a far better pick here, since the main point is you had to go from a place to another. Then you can specify how the movement was done (à pied = on foot). Same thing for the end (rentrer à la maison = to come back home)

aller faire quelque chose

"après" or "ensuite" would be more natural than "après ça"

"ramasser" to me kinda implies you were driving the vehicle; here, "aller récupérer" would be better

Les lumières surde l’autobus a fera couper[ont été coupées ?] à cause de la pluie, et j’étae me suis m’inquiétée encore plus parce que ma sœur est très petite, elle ne peuxt pas marcher enpar ces temps.

If you mean the lights were turned off => ont été coupÉES (passive structure)
"j'étais inquiétÉ" rather means you have problems because of other people
"temps" in the sense of "weather" is always singular, and "par" would be its preposition

Quand j’aie suis arrivée à l’école de ma sœur, la pluie as'était arrêtée.

Most movement verbs require the auxiliary verb "être" (except for those specifying how a movement is done, ex "I ran > j'AI couru")
Reflexive verbs also take "être" => je SUIS arrivée, la pluie s'ÉTAIT arrêtée

Lit. "the rain had stopped" (the downpour was already in the "state of being over" when you accomplished the action "arriver à l'école")

Si la pluie aurvait tombé encore, nous étions devrions mal, même sans lecontinué de tomber, nous [aurions été mal ?], surtout sans parapluies.

"encore" can also mean once again, so I'd use "continuer" here to disambiguate (continuer DE faire quelque chose)

Unlikely hypothesis in the past = "if A HAD happenED, B WOULD HAVE followED" = plusquamperfect indicative in the "si" clause, past conditional in the main one => avait continué, aurions été

I didn't really grasp the part between brackets. If you meant "we would've been in a difficult situation", "être mal" would work, although it's kinda colloquial
Also, you would've been in a bad situation ESPECIALLY without umbrellas, there is no contradiction here so => surtout

"without" in an absolute sense = sans (without article) => sans parapluies

Quelle chance !