First and foremost - speak with the rep at Schwab and ask for a pro at inherited IRAs. If they don't have one, then they're stupid, but they really should have SOMEONE there that can confirm all the moves you need to make. I had my accounts with Fidelity and they held my hand and literally did 90% of what had to be done - I had to fill out some paperwork, send in some letters/certificates, and answer some questions.
Make sure to set up the RMD as soon as possible otherwise you will be forced to take it all out within 5 years. You usually must take the first RMD by the end of calendar year, but make sure to confirm that the deceased took their RMD if they were at that age to be required - over 70.5 - because it must be taken on the deceased's behalf or else other penalties will kick in. Doing this way (over your lifetime) is referred to as a "stretch" inherited IRA.
Once the account is correctly titled as an inherited IRA in your name/beneficiary of XXX, any distributions taken out of this account will count towards your income, so if it is a large account, it could mean you are screwed as far as taxes for the years of forced distributions. I personally had my RMDs set up and automatically done with federal taxes withheld automatically and directed into my taxable account so I could then redirect it to my own and my husband's traditional IRAs.
Do not remove all of it unless you like paying more in taxes.
Once the RMD is in your savings/taxable/checking account, you may do with it whatever you wish. If you want to fund your Roth or traditional IRA, great. Spend it? Also great. Throw it in a taxable, super, as long as you already filled up the other stuff (Roth or traditional depending on which works best for you, if you can, max it out)... the one thing you can't do is put it back in the inherited IRA. That's why they force RMDs - they want you to get that money out of there, and it is a one way street.
RMDs are calculated based on your age and a percentage amount based on your life expectancy. So if you deplete it and it never grows (say you keep it in cash for some weird reason) then as you age, the amount should bump up each year since you are one year older, with it being depleted by the time you are "expected" to die. But if you have it invested, in most cases you'll see it grow and each year your RMD amount grows larger both because you're one year older AND the amount to draw down is higher.
That being said, you can still invest the money inside the iIRA in whatever you'd like and optimally you'd invest it well enough that it keeps growing. My iIRA is like an ever-filling bucket. No matter how much I pull out, it fills right backup and then some. I'm actually trying to pull more out now because it has grown so much that it's a fine line now between paying a tiny bit of taxes now, or having giant sized RMDs 10 years from now and owing waaaaay more to the IRS due to the RMDs growing as well. There are no penalties no matter how young you are (typically you'd pay a 10% penalty for withdrawing from an IRA before the age of 59.5). It is actually a pretty nifty account since the money grows tax deferred, but you can access it any time and in most cases it won't cause you to pay extra in taxes unless it is VERY large or you are right on the cusp of the next higher tax bracket.
That being said, I am so sorry you're dealing with this since it does mean you've lost a family member - my condolences.