Purple hair next week... Help!

1. Can you bleach/ lighten and color in the same day?

Yes. As long as she's using direct dyes (dyes that you don't mix with a developer). The direct dyes don't damage at all and are actually conditioning.

2. I have one week and although the forecast calls for rain, I'm putting my under-hair (if you will) in the sun with lemon and strong chamomile tea in an attempt to lighten it. It worked well on e top, so here's hoping it works under. Anything else I should be doing? I would rather avoid bleaching if possible

Really, the lemon and camomile does very little and does more damage than a gentle bleach because it's uncontrolled and you leave it in for ages. In fact camomile, I'm pretty sure, really only 'brightens' hair because it's toning out brassiness. It's not lifting at all. The lemon lifts the cuticle allowing the sun to bleach the hair faster. It's still bleaching. It being 'natural' doesn't make any difference.

3. I don't have the  time or money to keep up with a salon schedule. I go 1-2x a year and that's why highlights intimidate me. Can they be faded in and therefore grow out gracefully? Can I touch up my color with punked semi-perm every few months?

You could have bayalage type highlights put in. They're done in a way that looks more natural, Google some pictures of it. Yes, you can top up with a direct dye. Brands include manic panic, special effects, adore etc

4. Am I crazy for thinking that color will stick to my virgin hair without bleach?

Not crazy, but it doesn't stick well. It'll wash out faster because the dye needs slight roughness of the cuticle that bleaching gives to stick better. Also, it'll be brighter on lighter hair. You can certainly get a purple on the colour you have naturally, but it will be on the darker side and will need to be topped up more often. A gentle bleach will lighten enough and lift the cuticle enough that it'll be far more effective, look better and still won't be enough damage for you to feel it much if at all.

Thanks!
I meant to say Punky Purple, not punked. Oh well! It's the US version of directions, right?
Also, it's been about 5-6 months since I got my hair cut "short" and I hadn't seen any split ends until after my lemon experiment. Totally makes sense now!

Punky Colour and Directions are not the same, the two brands have no links, they just share some colour names