In the following sentence:
"I was working when you arrived."

The is clearly a PAST PROGRESSIVE.

But what is the ?

Can you consider it SIMPLE PAST or merely a PAST PASTICIPLE?

I used brackets so the sentence parts did not appear.

In the following sentence:

"I was working when you arrived?'

was working: This is a PAST PROGRESSIVE.

But what is: arrived?

Can you consider it a SIMPLE PAST or is it merely a PAST PARTICIPLE?

It is simple past.
"you arrived" - simple past
"you have arrived" - past tense using a past passive participle

Participles (when they're not being used before a noun like a normal adjective) are easily identifiable because they are usually parterned with an auxilliary verb (often to have or to be).

I hope that helps.

Craig