Interlaced Video Format 1080i (59.94)
You're not going to be able to replicate the precise "look" of 59.94, even with special plugins. This, due to the fact that interlaced is in many ways like:

Double Frame Rate - Half Resolution. 

Think of 59.94i at 1080 really as 119.88 at 540p. 

Interlaced lines are scanned odd lines first, then even. So you technically have a first set of lines which are actually one frame, with the other set of lines missing. These lines are then displayed back to the viewer odd/even//odd/even//odd/even etc. 

That said, you get smoother motion with i vs p. You are able to achieve better slow motion in post production with i vs p, however, p, is of course the preferred format to most. A single frame being a single frame. 

NOW THAT SAID...

Looks aside, in order to output your video from PPro, all you will simply want to do is import the footage material in (original); right mouse click; new sequence from clip; make any edits/trims, etc. 

It is really unnecessary to make any additional adjustments from the timeline in Premiere, because what you ultimately want to do is use Frame Blending when you export.

After you've made any adjustments, go to export, choose the format you need; 59.94i, whatever codecs they are requiring, many are already built in; others may need to be downloaded. 

Ensure you turn on Frame Blending, IF your source material is progressive. 

Frame Blending will force interpolation of the frames during the rendering of your new video outputs, using two side by side discreet progressive frames to create a new "quasi" interlaced frames, twice as many frames as your progressive source at the correct frame rate. 

It isn't quite the same "look" wise as actual Interlaced source material; however, specification wise it should meet their needs; and to the average viewer most will not notice. 

Do not however use Frame Blending if you are using Interlaced material. And do not double the effect by applying it to the clip in the timeline (which you can do by right clicking the clip; Under Frame Blending/Field Options); and then stack it with another Blend on export. Only one is necessary, and my recommendation is simply allow Adobe Media Encoder handle the p to i conversion. 

Lastly, if you have material at lower resolution, AME will be upscaling it to get to 1080. If so, you can use the Use Maximum Render Quality Checkbox at the bottom of the export panel window. 

Be advised this will likely increase your rendering time by multiple fold. 

In regards to the audio; they have peaking requirements. You will need to apply a Dynamics and/or Limiter filter in the Audio Mixer Window Filter Dropdown. Limit to the specifications they have stated. 

In regards to center safe, if you're given material that isn't center safe, you're going to need to talk with them about that, as you'll have to do a push in and do manual pan and scan using the motion filter, adjusting the frame position on the canvas to get it to 4:3 safe.