About this question you originally asked:
"Can [my sister] contribute to a ROTH, regular IRA and a 403b? Are totals cumulative or separate? I also believe she can contribute “catch up”? "
Teetee gave a partial answer in post #4 in this thread, although he talked about a 401k. For your sister's case, that will be replaced by the 403b.
So to directly answer your question, she can contribute to any/all of the 403b, Roth, Traditional IRA - although for the IRAs, there are some income limits she needs to be aware of.
The max annual contribution is separate for the 403b from the IRAs. For the traditional and Roth IRA, there is a combined max for the two of them.
For the 403b, in 2021 the max normal contribution is $19,500 with a max age 50+ catchup of an additional $6500 for a $26,000 total.
If she is able to contribute more than that, she can also do after-tax contributions (if the 403b plan allows it - some do, some don't). This is informally called a back-door Roth. The 2021 limit on after-tax contributions is $58,000 but this INCLUDES her other 403b contributions and any matching contributions. In other words, the TOTAL 403b maximum contributions of pre-tax + Roth + matching + after-tax is $58,000.
For IRA: There is a combined annual max for traditional and Roth IRA of $7000 (which includes the age 50+ catchup). So she basically should decide between the Roth IRA and the Traditional IRA and do one or the other. To reiterate, this IRA max is separate from the 403b max. The only other catch is, because she also has a 403b, if she exceeds certain income limits, there would be a further restriction on the IRA max. For more information about this, read here:
https://www.investopedia.com/ask/answers/07/401(k)_ira.asp
The main reason for doing Roth (403b and/or IRA) is if one expects to be in a higher tax bracket in retirement income than one is currently in. As another poster noted, your sister will probably not have a very high retirement income so it's probably better for her to do Traditional 401k & IRA contributions rather than any Roth.