Re: Can i install IOS 8.4.1 in Iphone 4s with 8Gb is memory?
Although I am not currently using the 4s, when I upgraded from OS7 to OS8, it was so much smoother with virtually no lag as experienced in OS7, almost on par wit my 5s. Apple must have done something about the memory management on older devices (I believe they recently did solve the issue of insufficient storage capacity when installing new OS)..
When it's upgraded to 8.4 (and jailbroken), there was a very slight lag but not by much. I do not know if this was the result of the JB (probably so). I have no idea about 8.4.1 but it is supposed to be a minor bug fix around Apply Music?
As to your question about the storage capacity, as long as you leave a bit of heap (perhaps at least 15% or so?), I believe the the effect of the storage capacity should be far less than the OS improvement. My 4s has 16Gb but only used half of it (not much music or other media, absolutely no game :-). If your intention to upgrade to OS8.4.1 is for the Apple Music and you stuff it with a lot of music, then I do not know :-). YMMV.