I’ll give it a shot (but keep in mind that while I grew up Catholic and am quite knowledgeable about the religion, I do not profess it myself… on the internet, you get what you pay for

)
This is a big,
big topic. We’re talking shelves full of books here. The more specific you can get, the better people will be able to answer your questions.
That said:
Salvation
According to Genesis, humans have fallen from their originally intended state of perfection and closeness to God. This fall is the root of human malice and pain, the ‘original sin’ which keeps us separate from God. As a consequence of sin, the gates of heaven were closed to us.
Humans alone cannot earn their way back in; the taint of sin remains, and its effects linger even after the blame is washed away by baptism. There had to be some kind of sacrifice to reopen paradise; and the only being capable of making such a great sacrifice is God himself. Hence the incarnation and crucifixion of the Christ. It is that sacrifice, Jesus’ death on the cross, that opened heaven to humans.
Given that we have free will, though, we can of course opt out of the promise of salvation by going ahead and sinning – denying or ignoring God’s love.
Purgatory
To understand this, you need to know the distinction between mortal and venial sins. A mortal sin is a complete denial of God’s love; without reconciliation with God (through the sacrament of confession) it’s a one-way ticket to hell. Venial sins are lesser, incomplete turnings-away from God.
Even after confession, the guilt of sin may be lifted but there’s still a thing called ‘temporal punishment’; you’re also due for it if you die in a state of venial sin. You aren’t going to hell since you repented and took advantage of Jesus’ sacrifice, but there’s still a smaller debt owed. Purgatory exists to purify souls of this temporal punishment before they enter heaven.
There’s plenty of scriptural basis.
This site has a nice collection of citations.
Mary above the angels
She’s basically the Queen Mum. Mother of God, after all – and the angels are God’s wait staff.
Intercession
Intercession, through the saints in general and Mary in particular, simply follows from the idea of ‘friends in high places’. It’s not praying
to them at all – it’s asking them to pray to God for you.