I was there in 2001 and again in 2010. I agree that things are more changeable in Russia than in, say, France or Italy, so evaluate my information with that in mind.
The first time, I got my own visa (since I live in New York, I could go to the consulate directly). The second time, they had changed the procedures; I tried but gave up, and ended up using a service.
On both trips, I was with my sister, who speaks Russian. In 2010 in St. Petersburg, I found enough English that I would have been comfortable on my own (with a guidebook). This applies to the central area and the top tourist attractions - Russia Museum, Church of the Spilt Blood, Hermitage, etc. As long as you learn the Cyrillic alphabet, you can navigate the subway (I've read somewhere that they are starting to put Roman alphabet signs in). Restaurants in the central area had English menus; even though not all restaurant staff spoke English, pointing to the menu worked fine. I say this as someone who doesn't always find lots of English when I travel (Spain is particularly notable in this regard; St. Petersburg without Russian is definitely easier than Spain without Spanish). However, outside of St. Petersburg and Moscow, I'd have been completely lost without a Russian speaker.
I see you've done some research on what you want to see. Some other places that were my favorites were the Russia Museum, Cathedral on the Spilt Blood, the Yusupov Palace, and the Sheremyetov Palace. If you go to the Russia Museum, don't miss The Wave by Aivazovsky - it's breathtaking.
While the Hermitage is amazing, it's also humongous, so your idea of spending two days there is a good one. We actually skipped it - deliberately - on our second trip, because it's so overwhelming. We did not get to the palaces outside the city (Peterhof and the Catherine Palace are the two most famous, but there's more).
In 2010 I stayed at the Griboyedova 29: http://www.hostelbookers.com/hotels/russia/st-petersburg/3991/. The location is fantastic, right near Nevsky Prospekt, the Metro, lots of restaurants, and many attractions (we walked almost everywhere). The bathrooms are not ensuite, but there are two showers and two toilets for 4 rooms, so we never had to wait. And for St. Petersburg, it was a bargain (we paid €80 for a double). There's a small kitchen, but we got breakfast at a nearby place that had breakfast specials for good prices (sorry, can't remember the name - it's across the canal from the hotel). Again, this breakfast place had English menus and the staff spoke enough English to take our orders.