Rollovers should not be subject to a penalty, because they are rollovers, not withdrawals.
Having said that... you keep on mentioning Roth IRAs. Rolling into a Roth requires that you pay taxes on the money in your 403(b), since that's now income.
OTOH, there's no tax (or withholding) if you roll the money directly from TIAA to Vanguard.
I've already maxed out the yearly contribution to my Vanguard Roth
You can rollover funds from a 401(k) or similar type account to a IRA without a tax implication as long as you don't change the flavor of the money.
That means Roth to Roth, and pre-tax to pre-tax. This will not cost you any money in taxes, it also doesn't count against your 401(k) or ...
I've already posted answers to your related questions, but since nobody has responded to this one yet, I'll take a stab at it too. Obviously parts of this will be repetitive.
This is a variation of the classic pre-tax versus Roth question. In general I lean toward the pre-tax side for most people. Since you mentioned your income is over the Roth limit, I ...
A separate traditional IRA won't allow you to avoid so-called "pro rata" taxes on a Roth conversion. In general the IRS treats multiple accounts of the same type as one, and this is certainly the case here. Look at Form 8606 - Nondeductible IRAs, where you would report your non-deductible contributions and conversions. For line 6 it says: