Good idea to walk backwards in a pool, as the water will keep you steady! I'm sure I couldn't walk backwards on dry land without stumbling--I'm a total klutz.
RE your question about when the gait starts feeling 'natural:' I am about a month ahead of you, and I can tell you that just in the last couple of weeks, walking has gotten easier. I'm not favoring the TKR leg as much, I don't have to watch my feet or the terrain as much, and sometimes during the walk I forget about the knee completely. Yes, I have had moments when the leg feels as though it could give way; notably, on a hill going down. But I think it's more my brain playing tricks on me than the joint actually failing--as soon as I note the sensation and stop to "test" the knee, it mysteriously solidifies and seems rock-solid. That's not to say that knees don't buckle. But that has not been my experience.
A few things that seem to help me with walking naturally: My husband is forcing me to go slowly in adding distance to our walks, which allows me to focus on my gait because I don't overdo it. If I want to go further, he goes with me at a later time. Another thing that has helped is therapeutic massage. My tight hamstrings, quads, and the popliteus muscle in particular, hamper my movement on the TKR side. The masseuse concentrates on these--also the IT band. Seems to help--he compares the good side and the TKR side and says he can tell I'm using both more equally now. That equals less limping! Finally, I think that multiple 10-minute uses of my little desk-er-cycle per day keep my knee limber and less likely to limp.