So very sorry for your loss.
Just know you can take a bit of time and let things ride a bit once you confirm they moved things correctly. It's really just three things, but may be a bit of paperwork/back and forth for them:
1. Get your account set up, labeled as a inherited IRA (BDA which means Beneficiary Distribution Account and just another way of saying "inherited IRA");
2. Confirm that your mother (if over 70.5 years old) took her required minimum distribution for the calendar year (if she passed in 2019, then it has to be done by the end of this year); and
3. Confirm you have set up to take your own RMDs (they can make an automatic distribution plan for you that takes care of the taxes and everything and you can change it or deactivate any time - just let them know).
After that, you could literally just let the account sit there until you feel less sad/overwhelmed and able to deal with things. I had a great guy at the beginning that literally walked me through everything I needed to do by phone. Taking a few months is not going to matter in the decades you'll hopefully be investing for, so don't put too much pressure on yourself to decide RIGHT THIS MINUTE what to invest in, and just get the required stuff done and take all the time you need to grieve, and then research your options.
As far as your questions:
Correct. FSKAX is the new one. They combined the investor/executive or whatever they called it levels into one fund and removed the minimum investment $ level. It's still great, has a tiny bit more distributions (dividends/cap gains) but slightly lower ER than Vanguard's equivalent so it comes out pretty damned close to even overall. Perfectly fine to use for total stock market index investing at Fido. This is what I use.
There is the new ZERO funds, you may or may not be interested in. They are considered loss leaders. They are literally zero expense ratio to buy/sell/own, and they offer them in the hopes that you'll also eventually be tempted to buy some of their other funds since you're already at Fidelity... but by just using Fidelity's low/no cost index funds, you're going to have the best possible outcomes. No cost to own/invest and the funds themselves are solid, extremely broad market index funds.
Fidelity ZERO Total Market Index Fund (FZROX), and funds like it, essentially invest in every single company listed on U.S. markets with only a few exceptions. This fund is as diverse as it gets, given it has about 2,500 holdings. Because it invests more money in the most valuable companies on the market, large-cap stocks make up the majority of its portfolio (the 10 largest stocks make up 18% of the portfolio).
It's new tho, so some folks are finicky about going into them since they haven't even been around a year or so, and you don't have to go for it if you don't want to. The good news is that since we're talking inside an inherited IRA, any buy/sell stuff is not going to trigger any taxable events. So if you decide a year from now you want to dump a chunk of FSKAX for FZROX, it won't cost you anything to do so.
So about the FZILX, you were asking... it's Fidelity ZERO International Index Fund. So yeah, same thing as above as far as decent fund. If you feel the need to have international in your asset allocation and it makes sense for your investor policy statement, then it's a decent, no cost index fund. I personally don't care about holding actual international funds and made the decision when formulating my own AA/IPS that I consider the U.S based index funds I invest in to operate internationally enough for me that I don't do a separate investment dedicated to singling them out. But that's me, and you have to decide for yourself how much you need international in your portfolio.
A few links that should be helpful on your journey forward:
https://www.bogleheads.org/wiki/Investment_policy_statementhttps://www.bogleheads.org/wiki/Asset_allocationhttps://www.bogleheads.org/wiki/Managing_a_windfall https://jlcollinsnh.com/stock-series/^can get this also in book form!
