Google Maps suggests about 20 minutes to walk from Park Guell. It's only just over a kilometre but I imagine some of the streets will be quite steep. Again Google maps gives a difference in altitude of about 90 metres. It's quite a good tool for this sort of thing.
You can walk. It's about 1.2km, partly uphill.
You can walk there quite easily. I would suggest the higher route that takes you past the Bar Restaurant Las Delicias, as you can walk through a nice wooded area all the way through Park Guell to the bar, then from there it's just a short walk to the Turo de la Rovira and Parc de Guinardo.
I'd suggest doing Parc Guell early. I have to say it's my least favorite sight in Barcelona, but if you're there early at least it might be a bit quiet, so there's that. Turo de la Rovira is a great choice.