Question

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?]

Answer 1

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.

<i>▸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...</i>