Hey there!

1) They will increase (very slightly) with every champion point you assign. The red star group is for health, blue for magicka, green for stamina, as usual. You don't get attribute points anymore though.

2) No, skill cost won't increase. On the contrary - there are stars (Magician and Warlord in the Tower) that reduce skill cost.

3) They won't get stronger per se - but just like during leveling up from 1 to 50, you're going to get "weaker" as your battle leveling decreases. Your stats are scaled to match the CP160 mobs now found throughout Tamriel, and that scaling goes down as you level up. So you need to make up for that with better gear, better skill rotation and overall playing skill. But worry not - this will come naturally as you continue playing.

4) There are several ways to improve magicka sustain, you already listed a few of them. You can use jewelry enchant (magicka regen). Put champion points in magicka regen/reduce magicka cost. Use heavy attacks to regen resources. Use a restoration staff and its passives for stronger heavy attack regen. If you're a sorc, use Dark Exchange to convert stamina to magicka (and health), and/or Energy Overload to recover magicka while attacking. Level up Alchemy (for the Medicinal Use passive) and use Magicka potions. In dungeons, have your group mates (usually the healer) use Elemental Drain or "magicka balls". In the end, you need to find a balance between resource sustain and damage that works best for you.