The route planner now(since update 1.1) will path up to 1000LY away, and you don't need to wait for it to path before selecting.
Just select the star you wish to travel to and if it is within 1000LY you can click the plan route button and it will set one up for you quickly.
The automatic route planner still takes a decently long time to build a web, though.
If the line that appears is solid you can make it there in a single tank. if the path becomes a dotted line, you will need to stop and refuel or scoop some fuel to keep going.
There are some tools people use to speed up the searching, but as with any third party app. Use at your own risk/discretion.
What are the advantages and the disadvantages of joining powerplay?
The advantages are that you get a weekly credit allowance (variable amounts), opportunities to prepare and expand your power's territories, and access to special bonuses that each power gives its loyal subjects. Your rank within your power is determined by the number of merits you've earned, and the rewards are different for each power.
The disadvantages are that sometimes it can affect the attitude of nearby AI if they have a negative relationship with your power. You may also find yourself outside your allied power's controlled space more often than you anticipate, and while that's not a disadvantage, it may leave you unable to take advantage of your power's bonuses, depending on what they are.
Can i still dock in systems exploited by others than Edmund Mahon?
Yes, though you may see hostiles or more forceful security patrols depending on where you are, and what the status of the other power's relationship is with your allied power.
Should I join it right now?
To cash in on the credit salary as often as possible, as well as earn merit points towards getting your bonus awards, starting sooner than later is probably wise. There's no punishment for joining a power and not participating, though, so you can go at your own speed.
The wikia has more info on how powerplay works in general but it is kind of overwhelming. Basically you just ally with a power, and you get some benefits simply by claiming your allegiance, and they're usually only beneficial when you're in your power's allied space. If you help with expansion and fortification missions, or just earn merits in general, the rewards and bonuses you receive are greater.
Best Answer
When you join or leave a wing, your position in the galaxy does not change. If you wish to group up with your friend, you will need to travel to them. Wing beacons only work within a single system, with a navlock range on the order of a few hundred Ls. You will not be transported across the galaxy and back when joining a wing.
Additionally, if your friend is in the starter zone, you will need a starter zone permit, which if you have any rank above harmless, penniless, and aimless, you won't have. Of course if they're merely around the starter zone you won't need a permit.