1. They were poor because they were not educated.

[Is 'educated' an adjective or a past participle? Is 'were educated' a passive tense? Or is it 'Verb + Adjective' structure?]

2. She wanted to help with their education.
[What is the meaning of 'with' in this sentence?]

https://www.grammarly.com/blog/verb-conjugation/

The charts here are very clear about the different verb forms in English. The auxiliary verbs "was" and "were" are used with present participles to form the continuous tenses; however, they are not used to form any past tense.

1. I'd take "educated" as a past participle being used as a predicate adjective to describe the subject.

2. The preposition "with" has MANY meanings! https://www.onelook.com/?w=with&ls=a Look at that list of meanings and uses at the right side.

It looks as if these are the closest to the meaning in that sentence you gave.

▸developing or improving as a result of something more...
▸used for saying what event makes something possible more...
▸used for saying what a particular action or problem is related to more...

1. In the sentence "They were poor because they were not educated," the word "educated" is an adjective. It describes the state or quality of being educated.

In terms of verb tense, "were educated" can be considered a passive construction. The verb "were" is the past tense of the verb "to be," and "educated" is the past participle of the verb "to educate." When combined, they form the passive voice, indicating that someone or something caused the action of being educated to happen to the subjects of the sentence.

2. In the sentence "She wanted to help with their education," the word "with" is used as a preposition. In this context, "with" indicates that she wants to assist or contribute to the process or progress of their education. It suggests that she wishes to be involved or play a role in supporting their educational endeavors.