1. Yes a tap is just as good for current as a splice, though not acceptable for digital signals or audio signals.
2. Most LED are not dimable. Depending on the type they may rapidly burn out.
3. Assuming they didn't change the design too much from the older models the wiring runs down the drive side a pillar to the fuse box, which is most likely where one would tap the wire.
To do this install correctly you would need to run wiring, determine the system amperage, possibly change the fuse, run the wire under the carpet or through the door (disassembling these door can be a project in and of itself) and modify the location of the lights in some manner to make them look good. While I intend no offence, your questions indicate this might be a first project for you, and may be more than you are ready to bite off. If its your daily driver I wouldn't recommend it. It its a spare, take your time, be careful, and have fun as you learn! If your not familiar with electrical work, please disconnect the battery cable as you work.