Do lower-difficulty Lockpicking perks have any effect on higher-difficulty locks

Making it "easier to cast" is relatively straightforward - it reduces the Magicka cost of the spell, meaning you can cast them more often.

This is similar to how things worked in Oblivion. (I'd link you to the UESP page documenting this, but the Site's still getting hit pretty hard from all the Skyrim traffic)

Each spell has a "base cost", which is modified by the following formula:

spell cost = base cost * skill multiplier * perk multiplier * equipment multiplier * dual cast multiplier
skill multiplier = 1 - (skill/400) ^ 0.65

This means that at 100 skill, spells cost 60% of the base cast (further modified by perks and equipment).

This isn't combat related, but as Affe has pointed out below, increasing your magic skills is required to buy high-end spells from vendors.

From what I gather they appear generally every 36 or so hours. I tend to find them in towns when I'm waiting for shops to open.

I read somewhere that you can sleep for 36 hours in a town and when you go out a dragon spawns every time.

Also you need to do a quest in Whiterun as part of the story to allow attacks by "wild" dragons.