You need to be rooted and use the app stick mount which is free from the play store to use otg. IINM la cause it doesn't support otg out of the box. Alternatively there's an app nexus media importer which you can use if you don't want to root. It is a paid app though.

What type of file is your video? Some codecs still not fully supported in Android. Try using mp4 files

Yes but this is not windows where you can install codec packs Most of the video players from playstore use software decoding for files which are not supported. Thats why sometimes certain files especially HD ones will lag if the codec not really supported. Can play is can play but it will lag. I use MX Player btw by far the most reliable one IMO

If what you meant was launching the search function in the home screens then need to install GEL (google edition launcher). That feature is actually "exclusive" to the nexus 5