Think the hotel/apartment thing is just so you don't get ripped off.
If you can, try to get somewhere closer to Maidan - Shouldn't be too hard to get a flat other side of the square to Hotel Ukraine.
Taras Shevchenko Park is about 5/10 mins depending on walking speed. Not a big issue really. Probably about as far away as Hotel Rus is to the square.
If you walk towards the square from Taras, on the other side of the road is Katyusha restuarant (about the Roshen shop) food is great there.
To be honest, I've never had a bad meal in Kiev. Mama Manana is considered one of the best. Very nice in there.
Kiev is just as safe as any other european city. I've walked home absolutely hammered before now with no problems - police even helped me get into the apartment.
There are lots of clubs but we really only go to Ugly Coyote. Visiting a gentlemans club appears to be a national passtime. Scarletti opposite Hotel Rus is our favourite.
There is Uber in Kiev but locals use and prefer Uklon. Metro is cool to use and very cheap. Arsenelna is the deepest metro station in the world. From there you can walk down, visit the Holodomor museum, have a look round the monk village (it's a little bit like the vatican only much smaller!) and carry on to the Mother Monument. Walk back and opposite the Holodomor museum is a great bar for food and a drink. If you sit outside and it's not too cold, they provide blankets to keep warm. That's a day taken care of no problem.
I've not done a day tour to the zone. The group I go with isn't as well known as the others but I believe we get to do a lot more.
I'm running a trip of my own end of May. There is a really nice RC buggy track in Kiev and we are holding a race weekend - East Vs West Europe. This trip will include a day tour.