I stumbled across a cute local tea store and whether this tea set was practical, I didn't care - they're my favorite color and they were practically screaming for me to pick them up and take them home. I think I get this from my mom.

Anyway, I'm pretty new to tea and my exposure to exclusive shops in person is pretty minimal, so I was excited to see what they offered. This particular tea shop seemed to have more of what I'd call a very "tiny" size of either Chinese teacups or teapots (mostly yixing, I am assuming at this point) and I'll admit I was a little embarrassed to ask in person if this size was practical.
Please forgive the crappy shots and lighting... it's almost 3am here, but pictures are fun to look at in these threads

I did some quick measurements and the tiny cup can hold a little over 1tbsp (15mL) and is about 2in wide. What is this used for?? Tiny shots? I tell myself it's pretty strange because I'm used to drinking out of 12-16oz mugs and stuff with a mesh basket but I don't know. The cup with the cover (gaiwan? correct? Though there isn't a saucer for it) holds a little over 6tbsp (90mL), and so does the pitcher. Thoughts? I don't have a small teapot to use with this set - I have a ceramic one that's like 12-16oz, I forget. I also managed to score a small tea table I would like to use that so I studied up on it a little.
A couple questions un-related to the above:
-Say you brew a single moderate sized cup of (x) tea at night, but you feel like stopping or switching to another tea (y). There are still infusions in (x) tea, and you don't want to waste. Do you just let the leaves sit in the pot/mesh basket/etc in some of the leftover tea water, or drained (with a possibility of them drying out, even) or something else?
-Is there a way to make matcha somewhat properly in a bigger bowl, like is it supposed to foam at all, or is that not supposed to happen? That's all I had, and mine didn't foam, really... I have the chasen and I watched a couple demos, but what I got wasn't what I expected, I guess. Also I didn't like the taste of that particular matcha, but I know I used a little too much of the powder for sure, so I want to try again... Try, try, try again.



EDIT: I remembered one!
-The tea table is bamboo. Granted, it seems like it'd be convenient to use, but I was wondering how to care for it aside from dumping the water out and rinsing it a bit. Mainly, does yours stay wet most of the time? OR do you (purposely) let it dry out? Are you supposed to? I guess it would if you left it alone, but is it "not suggested?" Um, and since I was curious... the one I have is deep enough to actually hold these tiny pieces of teaware. I feel stupid asking this, but would it be even remotely OK to keep them in there? (with the top part with the slots open, of course).
I do want to add that my experience to the small shop was a great mood lifter for me. The lady was chatting with me for awhile and I had bought a cup to try something new. She was drinking a pu'erh in a cute small cup from a tiny yixing pot and I got to try some for free... but I really enjoyed it so much. I was having such a crappy day up 'til then, but ahh... the tea and conversation really helped to lift my spirits up.

Thanks for reading, I really appreciate it!