Has there been any cryptanalysis of RC4-52?
Well, I have unaware of any specific analysis of RC4-52.  The closest thing I can think of is Cryptanalysis of RC4-like ciphers, which is an early paper which explores RC4.  Of particular interest would be section 5 (Tracking analysis), along with Table 4; that explores the obvious way to attack RC4-52.  Now, I suspect that it could be improved modestly (say, by attempting to search for a Fortuitous State, see section 5), however I suspect that won't gain you all that much unless you have huge amounts of keystream available).