DisplayPort is compatible through all of these connections via different adapters:
DisplayPort to VGA
DisplayPort can be adapted to VGA with an active adapter, as it does not output an analog signal as standard. Note that most of these do not require additional power, and receive sufficient power to function from the DisplayPort itself.
DisplayPort to DVI
Things get a little more complicated here. DisplayPort does not output a signal compatible with DVI as standard, but can be adapted to do so. The type of adapter required varies based on whether you have Dual-Mode DisplayPort (DP++).
For versions 1.3 and above, or DisplayPort via ThunderBolt, this is always present. You can look for a DP++ symbol (above) by your DisplayPort, it would usually be present if your machine has this.
If you do, you can use a simple passive adapter from DisplayPort to single-link DVI.
For dual-link DVI, or DisplayPort without DP++, an active adapter is required, which may require additional power (Often from a USB port).
DisplayPort to HDMI
Again, this varies based on if you have DP++ or not. With it, you will be able to use a passive adapter.
And without, an active adapter would be required, although these are able to draw the power requirement from the DisplayPort.
Note that when using multiple monitors, you may need to use active adapters depending on the video card and it's capabilities over DP++
Looking at this spec list for your model, your machine is equipped with DisplayPort 1.2. As such, it's not guaranteed you have DP++, but still possible, check the port itself to see if the logo is present. If not, you can still do it but will need an active adapter, although these are usually a little more expensive.
For your other question, the adapters will let DisplayPort know what source they require, and will adapt voltages to make sure the correct signal is coming through. You won't need to change any settings for this.