At your level the issue isn't really looking ahead, I suppose the issue is rather the recognize cases and actually do the moves. If I were you I would already start to learn the 4LL algs on the side ( one a day is good if you're still working on F2L intensively ). Also try to time your cross. I'm sure at 2mn you probably take anywhere between 10 and 20sec. With a bit of practice you can easily drop it to 7-10. So if you're confident with the last layer with the beginner method, I'd almost stop solving it for a while. Learn 2 look OLL/PLL, and focus on F2L ( so cross included ). For a week you might not feel the progress, since your LL will be a "work in progress", but as soon as you reach it, with your improvements on F2L, you'll be doing a jump. This should put you close to 1mn already.
Also, about progress, it all depends on the time you have. The more time the better of course, but the most important is to do at least a little bit every day. I'm pretty new as well, I was pretty much at where you are a month ago, I average 40.xxsec at the moment. My target was to get sub 60 for christmas, I finally even managed sub 50 for christmas.
And for the zhanchi, for mine I used to set it quite tight when I first got it, after a few days of solves sexy moves and LL algs, it got well broken in already which made it somewhat a little slower and smoother ( less clicky ), which really pleased me.
All in all, welcome and good luck !
And .. practice .. practice .. practice
