Question 1. Can I roll just the newly deposited 11k over to ROTH? (To avoid paying cap-gains)
The pro-rata rule makes it so that if you convert less than all of your traditional IRA balance to Roth, the conversion will be prorated based on what fraction of
all your traditional IRA accounts is pre-tax vs. post-tax.
You have $29k in your traditional IRA, $23k of after-tax contributions and $6k of growth. If you add another $5.5k tomorrow, you'll have $28.5k of post-tax basis (82.6% of the total), and $6k of pre-tax growth (17.4% of the total).
You're allowed to convert any fraction of your $34.5k to Roth. Whatever amount you convert, 17.4% of it will be taxable income due to the pro-rata rule.
Question 2a. Should I just roll the entire 58k over? The gain on mine is 6k (so lets assume 12k gain total)
Probably. The pro-rata rule means you're paying tax from the first dollar of the rollover, and leaving money in the traditional IRA just means that the money will have more time to grow in there (where growth is pre-tax) instead of in Roth (where the growth is post-tax). An exception might be if you're close to the top of your current tax bracket, you may find an advantage to splitting the conversion between two separate years.
Question 2b. Am I correct in assuming I only pay taxes on the 12k as cap gains? (15% * 12,000 = $1,800 in taxes?????)
You only pay tax on the gains, yes, but it's taxed at normal income tax rates rather than capital gains rates.
Question 3. How bad did I mess up here?
If you had converted immediately you would have had that $6k of gains be in a Roth account where you will eventually be able to withdraw it tax-free, instead of in a traditional IRA where you still have to pay tax on it. Multiply $6k by your tax rate. A somewhat expensive lesson, I suppose, but probably shouldn't set your retirement back too much.