OK, I'm not going to re-quote that whole thing, so hope I don't miss anything. :-)
1. If it were me, I would start fresh on the receipts and tracking and such (again: lazy!). The important thing is to get a baseline of your "normal" spend so you can plan going forward. One thing DH did to deal with cash was he just allocated it when we took it out of the ATM, based on what we usually spent cash on -- e.g., $200 withdrawal would maybe go $125 to food (he eats lunch out) and $75 to entertainment. It's not $100% accurate, but he wasn't willing to track every $1.98 receipt, so it was better than the alternative. Also, I've heard some people like YNAB more, because it allows you to allocate money for different future needs (so you have different mental "pots" of money, even if all of that money is sitting in the same account). The trick will be to find whatever works for the way you operate -- there's no objective "perfect" here.
2. The main issue you have is that you are asking a lot of questions that depend on how much money you have and what your expenses are -- and so no one can really answer that until you get the expense thing under control! So, for example, your EF: having $3K on-hand is awesome for before your first paycheck, so you are probably good for the immediate future. But long-term, many people advocate for anywhere from 3 to 9 months of living expenses in an EF (you are young and single so can probably get away with 3 mos.). So once you figure out your expenses, I would suggest contributing some money each month to the EF to build that up -- but how much is going to depend on how much you have to save, what your expenses are that make up that 3 months, and what your other savings priorities are (401(k), IRA/Roth, sinking/future purchases fund).
3. In terms of IRAs: I am a fan of IRAs and Roth IRAs, but I think your first priorities are your 401(k), your EF, and your "sinking/future needs" fund. The reason is, quite simply, that there are various rules for IRAs and Roth IRAs that can make it complicated for someone just getting going -- if you are covered by a 401(k) and make above a certain income, you can't deduct an IRA contribution, for example; if you make more than a different amount, you can't contribute to a Roth (but you can open a non-deductible traditional IRA and roll it over to a Roth); if you are eligible for a traditional or Roth IRA, you need to do math to figure out which is the best choice; etc. The #1 principle here: don't let the perfect be the enemy of the good. Yes, put "figure out IRA options" on your list of things to learn! But meanwhile, start socking money away in your 401(k) and your EF/sinking fund. You can put up to $18K/yr into your 401(k) -- that's a lot of money! It is most important to get going on that now, while you take time to figure out all the other stuff that is more complicated.
4. Investment choices: "Asset allocation" is how much of your money you put in stocks, bonds, and other asset classes I'm going to ignore for simplicity's sake. Many people will do something like 80% stocks, 20% bonds, for example. Since you are young, personally, I don't think you need to worry about bonds if you don't want to (although they do minimize your downside risk, so if you are scared you would sell off in a slump, you should have some bonds). Once you figure out how much you want to put into stocks and bonds, you want to invest that money into low-cost, broad index funds or ETFs. The Vanguard Total Stock Market Index fund is an index fund that, basically, covers the total stock market. So what I was proposing was a 100% stock asset allocation, because of your youth. OTOH, if you want some bonds, Vanguard also has a total bond market index. Make your life easy, and just choose those two Vanguard options, in whatever proportion feels reasonable to you. Remember, you can always change it later when you learn more!
However, most of your investments at first will be in your 401(k), which means that you will be limited to what your company offers. If they offer a Vanguard or Fidelity broad stock market index, choose that. Otherwise, look for the lowest-cost broad market index funds they offer.
You asked about whether it would be better to put money into your 401(k) beyond the match or put it into "investment" -- the thing to realize is that those are both "investments." Think of your 401(k) or your IRA or your regular taxable investment accounts as "buckets" that you can hold money in. Within each of those buckets, you can choose a wide variety of investments -- stock funds, bond funds, money market funds, individual stocks, precious metals, you name it. So in your 401(k), for example, you can "invest" the money in a stock or bond market index, or you can "save" it in a money market or cash-equivalent. Because this is long-term money, you should be investing it for long-term growth.
This also means that with your own investment accounts, you are not tied to any particular company. So for ex., your parents opened a Roth IRA for you with someone, and they put that money into an "18 month" variable whatever. I have no clue where that money is or what that is -- and it doesn't matter! If you open your own traditional or Roth IRA, you can choose your own investment company (Vanguard, Fidelity, Schwab, etc.), and you can have them open your own IRA/Roth, and you can put up to $5500/yr into whatever funds they offer that you choose. The only key is that you and your parents combined cannot put more than $5500 each year into an IRA/Roth. So if the Roth they set up for you comes from past years, you are good to go and can call up Vanguard and set up your own IRA/Roth for up to $5500 this year; OTOH, if they are still contributing say $2K/yr to that Roth, you would be limited to putting in another $3500/yr -- but you could still invest your $3500 with any company you choose (hint: Vanguard).
So, tl;dr: Vanguard, Fidelity, Schwab, etc., are all investment companies who sell products. Those products can be stock funds, bond funds, money market accounts, individual stocks, etc. etc. etc. They will also hold those products in whatever kind of "bucket" you want -- a regular taxable account, a traditional IRA, a Roth IRA, etc. For your 401(k), you must use the investment company your firm has chosen, and so you will need to limit yourself to the funds they offer. But for the money you are saving/investing outside of your 401(k), you can choose whomever you want (Vanguard).
Start with your 401(k) and cash-type savings. Put your 401(k) money in the lowest-cost broad market index funds your company offers; put your EF/sinking fund into a savings account or money market fund at Vanguard. Once you learn about IRAs/Roths, open one with Vanguard (assuming you are eligible) and put that money into low-cost broad market index funds too. If you still have money to invest, go back to Vanguard and buy the same broad-market index funds in a regular taxable account. That's it. The "investing" part doesn't have to be any more complex than that; the hard part is figuring out how much to invest -- and then maximizing that amount. :-)