Your question begins saying the person came to the US in 1948 "for a visit." This may be the factor determining the answer.
US visas (as documents) date from 1924 and include both immigrant (permanent) visas and NONimmigrant (temporary) visas. The immigrant/permanent records are for those admitted as immigrants to live permanently in the US. The NONimmigrant visas are for those admitted temporarily, such as "visitors for business or pleasure." And while we see the records of many NONimmigrants in the passenger lists and passenger arrival records on microfilm and digitized online, records beyond the manifests (like visas) followed a general records management rule: Records of permanent admissions are permanent, records of temporary admissions are temporary (destroyed).
What this means is that when a visitor arrived in 1948 they were documented (by INS) at least on an I-94 showing nonimmigrant admission (usually 3 to 6 months, and could be extended). When the visitor departed, the arrival and departure records were married up to verify departure/compliance. The records might be microfilmed before destruction, or may have just been destroyed. Temporary records.
Any arrivals that had no departure record by the date they were required to leave became an "overstay" illegally in the US. That record was retained long enough to locate the overstay and arrest/deport them. If it came to that, since 1944, everything would go into an A-file.
Any records of the NONimmigrant visa application process would have been generated/collected by the Department of State. I know some researchers have been having some luck searching visa issuance matters in DOS Consular records at NARA in College Park, MD, but I'm not sure those records are available for the post-WW II and later era.
Not a complete answer to all your questions but I hope it helps a little,