When drawing a simple circuit, does the loop direction matter?

You've got it right, and the good news is you can't really get it wrong. For a simple series loop like that, the drawing works no matter which way the battery symbol points or which side the switch sits on. The long line is the positive terminal and the short thick line (often with the little plus sign) is the negative, so keep that consistent within your own drawing, but a bulb and a switch don't care about polarity. Current goes either way thru them just fine. The only time orientation starts to matter is when you add things like LEDs or a meter, which do care which way round they're connected.

On the 'which way does the current flow' question, the answer you probably want to give your kid is that there are two conventions and both are fine. Old textbooks say current flows from the positive terminal, through the circuit, back to the negative. Physically it's electrons drifting the other way, from negative to positive, but engineers still draw it the old way and everything works out the same. The loop thing is actually the key idea: nothing flows unless the path is complete, so opening the switch breaks the loop and the bulb goes dark. That's a nice demonstration to show them, flick the switch and watch what happens.

For the second bulb, just draw it in line in the same loop, exactly like you described. That's a series circuit, and it's worth pointing out to your kid that both bulbs will be dimmer than a single bulb on its own, because the battery's push is now shared between them. Also, unscrew one bulb and the other goes out too, since the loop is broken. If they want both bulbs bright and independent, that's the parallel version, where the wires branch so each bulb gets its own path back to the battery. Drawing that one is a good follow-up project, it's just two loops sharing the same battery.

Funny timing, I just did something similar helping my nephew build a little quiz buzzer box, and the thing that saved me was drawing the wires with a ruler so every corner is a proper right angle. My first attempt looked like spaghetti and even I couldn't follow which wire connected where.

One thing I'm still fuzzy on from that project: if the kid later wants to try that parallel version with the branching loops, does the battery symbol stay the same or does it need drawing differently when two loops come off it? probly obvious to everyone here but I genuinely don't know.

We actually tried the two-bulbs-in-a-row thing with a couple of little flashlight bulbs and some tape, and sure enough the second one made both of them glow weaker. My kid was annoyed at first untill I pointed out they could touch the loose wire to either bulb and make a shortcut path, and then that one lit up bright on its own. Kind of accidentally did the branching version without knowing it had a name. One thing I kept wondering though: if both bulbs are sharing the same battery, does the battery go flat quicker than with just one bulb?

One pedantic detail I always add when sketching these for my daughter: put a little arrow next to the wire showing which way you've decided the current goes, with a note saying it's the conventional direction. It sounds fussy but it stops the arguments later, because when she drew the arrow the other way once and the bulb still 'worked' on paper, we had a genuinely useful chat about why both answers can coexist. Also, strictly speaking one long line plus one short line is a single cell, so if you draw two pairs of lines back to back that's technically a battery of two cells, though for a school diagram nobody will mark you down either way.

One thing that trips kids up at this stage is the idea that current gets 'used up' as it goes round, so the bulb nearest the battery is brighter. If that question comes up, tell them it's more like water pressure in a sealed loop of pipe, the flow is the same everywhere in a series loop. I've been drawing panel schematics for 14 years and I still label the battery voltage next to the symbol, in this case just write 1.5V or whatever the cell is. Makes the diagram look official and gives you something to point at when the 'push' question comes up.

Update: took the ruler tip and redrew the whole thing, corners square, arrow added like one of you suggested with 'conventional direction' written next to it. Then we wired the two bulbs in a row like the other poster described, and yep, both went dimmer. My kid now wants to know where the missing brightness actually goes. Is it just spread between the two bulbs, or is something lost along the wire?