1. I didn't get a bottle before doing the skip, mostly because I wanted to see if I could actually do the skip. This means I am bottleless until I manage to make it back to child Link, yes?
Yes. Three bottles can only be obtained as a child, the fourth requires a bottle, and all bottle duplication tricks require having a bottle in the first place.
2. I didn't get early Chus. So I'm a bit lost on what I should do for bombs because my goal in terms of getting back to child Link was to use the knife clip. What's the most expedient way to do this? Can I even do this? I admit that I haven't played this game in quite some time so it's hard for me to sequence things in my head. I am watching runs to help me out though.
It's possible. Your best option for Bombchus is to collect 10 skulltulas to obtain the Adult's Wallet, then buy them from the flying carpet salesman. You can get to Gerudo Fortress with Epona, or either the Hookshot or the Longshot, but getting across with the hookshot is almost inhumanly precise. To get across the desert, you're suppose to use the Hoverboots or the Longshot to get past a spot of quick sand, but you can just pull of a certain backwalk to get across.
Also I recommend checking out
http://zeldaspeedruns.com/oot/generalknowledge/items-and-power-ups, and not because I wrote most of it. It has a bunch of general information on all the different items in the game (like chu locations), all in one place.
3. On the subject of bombs, I'm getting pretty solid at SS with a single bomb but I've noticed that botching a SS attempt seems to lock my action icons (C items, sword) from being used. This is a result of letting the bomb damage me?
A failed superslide attempt can put you into a state where you store what is known as a ground jump. It's not because of the bomb damaging you. When this happens, simply sidehop or backflip: This will trigger the stored ground jump and you'll be able to use your c-items/sword again.
4. And finally, getting to the DoT skip, I was curious how people generally went about the roll into the sidehop. Getting the clip while using my thumb proved tricky but if I mash with my index finger, I'm far more likely to succeed. Is this common? Does it matter?
Don't know, but I expect someone else will have the answer.