No. Table top basins have a flat bottom designed strictly for resting on a counter. They do not have holes in the back for wall bolts.
It depends. Some models have a “Tap Landing” (a ceramic platform for the tap). Others are just a bowl, meaning you must install the tap on the counter or wall. Check the model spec.
If installed correctly with a thin bead of silicone, dirt won’t get under it. Just wipe around the base with a cloth where it meets the counter.
If you pair it with the right tap, no. Ensure the tap spout aligns with the center drain of the basin to prevent splashing.