Guys, thanks for all the advice. We had good time overall, but I have to say the public transport situation for us (as a 6-7hr visitor) was incredibly difficult. I just can't understand why they can't make it easier, like HKG.
I went to get the Clipper card at the airport info booth. They said I should just do single-ride tickets for my situation and told me to buy it from the BART station vending machine. So off we went. I'm trying to figure out the machine at the SFO BART station... it gave me weird options like 'buy a $20 ticket,' 'add value,' 'deduct value.' I wanted to buy a ticket for $9-something to head downtown, but I couldn't figure it out. So I went to the manned booth to buy it from him, but he tells me I have to buy it from the vending machine. When I told him I couldn't figure out how to use it, he gave me a total attitude. I eventually talked to someone else and figured it out, but then I also found out that the kid's ticket had to be bought at that previous info booth. Somehow the adult ticket is only available at the BART station vending machine while the child ticket is only available at the airport info booth.
After we did a couple things in the city, we headed to the California St cablecar. Once we got there, we found out it was closed for maintenance! I did a lot of reading up on the cable car beforehand, but nowhere did I see any notice that the California St cable car wouldn't be operating for a few days. That completely unraveled our plans, as we then were ready to scrap the remaining plans in order to instead go ride the Powell St cablecar.
We caught the Powell St cable car at its starting point at Powell & Market. Luckily we only had to wait 30min for the Powell St cablecar. The website I saw seemed to indicate one may not be able to get on the cable car at non-start/end points, since they often get full right from the beginning. So we just went to the starting station and waited in line. However, they weren't letting enough people each time so that each train was leaving with lots of space still available. Then they'd pick up other folks 2, 4 blocks later, and they get to get on without waiting at all.
Heading back to the airport on BART, we got on the southbound train at Powell St. You can hardly make out anything they say on the PA system, so I didn't even know where our train's final destination was. But I figured all the southbound trains were going to Daly City (based on the BART map), so we would just get on it and at least ride to Daly City and then see what happened there. Well it turned out the train went another few stations (like 16th or 24th? station or something), then suddenly made a U-turn and began heading back towards where we came from. We then had to get off, figure things out by talking to people, etc.
There was also one puzzling thing that worked to our advantage. I read that you should keep your MUNI transfer slips, because they can be used for 90min. However, the transfer slip indicated a time that was more like 5 hours after my boarding time. I was skeptical that the transfer slip would let me ride another bus ~3 hours later, but indeed I showed the driver when getting on and he waved us through.