No it doesn't use an SD card. They use special PSVita Memory cards, which are sold separately.
Vita games come in both physical and digital form. Physical copies of games can be bought wherever you can buy video games, and are stored on a small proprietary flash card, much like those used for the DS and 3DS. These games can also be bought and downloaded off the Playstation Store.
No they have a new system of proprietary flash memory cards, similar to SD cards, called 'PlayStation Vita Cards'. Unlike a UMD, the Vita can save to these cards, space is reserved for game saves, user settings and patches.
Assuming you mean the PSVita Memory Card (the only card it supports, it does not support any kind of SD card), the card goes into a small slot, covered by a movable panel at the bottom of the PSVita.
no
In general, very few to no SD cards come with SD card readers, which is to be expected, as CD's don't come with CD players, etc.
There isn't, as far as I know. Did your micro sd card not come with a regular sized sd card adaptor? If not, you will need one.
Some cameras come with an SD card, but if you're planning on taking a lot of pictures you should purchase another SD card.
No, both use proprietary memory sticks made by Sony. The PSP uses the Pro Duo memory stick, the Vita uses a PSVita Memory Card. This is not the same as a Micro SD card and it is not compatible with one.
No it doesn't. But it does have a slot for it.
Check
It will most likely not cause any harm to the SD card readers to apply tape on the SD card beside a faulty write protect switch as long as the SD card still fits easily into the slot and does not peel back or come off.
You have to buy it yourself