1) Much of the footage I receive to edit is in a 4K format,  when setting up my project what is the best format to choose?   Should I really be trying to encourage the use of 1080P?

It is good to work with 4K footage as it has more detail but may cause your system to lag if you don't have  a fast graphics card/processor/RAM. 

Usually, if the majority of my footage was 4K and, even if my intended output was 1080P (which it usually is), I would still work in a 4K sequence so that my system does not need to convert it on the fly which in turn would slow my system down. I can always down-size it to 1080 on export if I want.

2) Certain video clips I’m importing are at different frame rates, can’t remember if this is ok or whether I need make them the same?

Premiere Pro can easily handle footage of different frame rates within the same sequence timeline. Again, I would set my sequence to the frame rate of the majority of the footage (if no specified frame rate was required: like for web).It is more ideal to have all footage share same frame rate as, due to the complex mathematics of frame rate conversion, which may cause occasional frame jitter as frames are either dropped or duplicated. Conversion of higher frame rates (50fps +) gets a better result but we don't always get that luxury.

3) I’m having a problem where my footage is coming in with sound but the sound and videos are moving independently of each other – am I able to turn off this function so that they don’t fall out of sync? Linking doesn't stop the footage from moving independently?

It sounds like you have Linked Selection turned off. Here are 2 ways to turn it on:

  1. In the top menu bar choose Sequence > Linked Selection ... or
  2. In the top left hand side of the timeline check the Linked Selection toggle button

Now any clips in the timeline will automatically linked to their corresponding audio. By default it is turned on so you maybe accidentally turned it off.

4) I can record (using the record action capability) a brush tool on Photoshop drawing a picture in CS6. It can then replay on photoshop as an action, each stroke appearing in turn to draw the whole image. Is there a way to export that recording to Premier and After Effects so I can then play around with the recording time, zooming in on the areas being drawn, panning across with the line, etc?

The simple answer is that they need to use a separate screen capture program (like Adobe Captivate or Camtasia) to record what they are doing as a video. You can then import that video into After Effects and Premiere Pro to edit and animate zooming etc.

5) Can I export en animated GIF from After Effects or Premiere Pro?

No, to do this export a video (As Quicktime) and then open it in Photoshop and export that as an Animated GIF. 

Open the video in Photoshop then choose Export > Save For Web. Then choose GIF format with Animation.

6) I'm currently putting video togther which is 4K footage,  however I have some 1080P footage I want to use but when i import these files they are scaled down  so i have a black border around the video,  how can i change this?

If your intention is to export at 1080 then right-click on the clip and choose Set to Frame Size - this will scale the clip up to the 4K size. It will look slightly more pixelated than the 4K footage but when you export it will conform to it's original size and the remainder of the 4K footage will be scaled down. If your output is intended to be 4K then I would be wary about scaling the 1080 clips up.

7) I want to edit a person out of some footage they are hidden but not enough and we can make out the person, dont really want to use blur effect, was wondering if importing into photoshop would be better but cant find how i can do this as its greyed out?

If your camera is still (on a tripod) you can export a frame by clicking on the Export Frame (Camera Icon) button on the Program Monitor (Shift + E (Mac) or Ctrl + Shift + E (Win)) Choose PNG and Import into Project. 

Then open the image in Photoshop, clone out your person however you like and then delete the rest of the frame to make an alpha (Transparency) channel (this could be more efficiently done if you have a frame that does not have the person in it so no cloning is needed.)

Back in Premiere Pro, add this image to a track above your video and the person will be hidden. Check through the frame that the person does not move out from behind the image and also that no other foreground people hit the edge and go behind it. If there is camera movement in the shot this will obviously be more difficult and would require work in After Effects.