We went to the store --

what are

we

went

We is a pronoun and is also the subject because it is the one doing the verb - we went.

went is a verb

Agnes is a great person.

What are

is

great

is = verb. Agnes isn't doing something, but she is something.

great = adjective (describes a noun -- person -- what type of person)

While we were at school, we studied hard.

What are

at

studied

hard

At is a preposition. It begins a phrase that tells where we are -- at school.

Studied = verb.

hard = adverb (it modifies a verb -- how hard we studied)

Agnes' horse is on the ranch.

What are

horse

ranch

Horse is a noun and is also the subject of the verb "is"

Ranch is an object. It is not the subject doing something but the object of the preposition "on." It is on the ranch.

On Friday, he went there, and he did it.

What part of speech is each word in this sentence?

In addition which of the three clauses are dependent and which are independent?

On = preposition

Friday = noun and object (of preposition on)

he = pronoun and subject of verb went

went = verb

there = noun (it is a physical place)

and = conjunction

he = pronoun and subject of idid

did = verb

it = pronoun and object (of verb did)

"On Friday" is a phrase. It is not really a clause because it has no verb. It cannot stand alone.

"He went there" is an independent clause.

"He did it" is an independent clause.

"And" is simply the conjunction that joins the two clauses together.