Another noob question here: is my balance on the bike going to improve with time on the bike or do I need to practice this skill to improve it? Don't feel out of sorts around corners and such, but even simple things like pulling out food and opening packages makes me nervous, and I'd never try putting on or pulling off a jacket while moving. I did recently move up to larger continental 4-season tires (was riding bananaskins) so that should help some, but that won't solve poor balance.
If you have a local park or something, you might be able to find somewhere quiet to practice. I wasn't happy with my descending so in the absence of any decent switchbacks to practice on here, I found a circuit in my local park and did some laps to practice cornering, and as @Black Belt Jones says, looking out of the corner rather than into it. You could also practice getting things out of your pockets and stuff. In the meantime, if that is an issue, you can always use a bag on your top tube to put some food in.











