Gary L. Bauer, President Reagan's nominee to be undersecretary of education, yesterday fielded tough questions from a Senate panel on topics ranging from school desegregation to abolishing the department.

No date was set for a vote on the nomination. But afterwards, Sen. Robert T. Stafford (R-Vt.), who chairs the Senate Labor and Human Resources subcommittee on education, said the hearing produced no surprises and that Bauer probably will be confirmed.

Bauer, a former policy analyst for the 1980 Reagan-Bush campaign, now serves as deputy undersecretary for planning, budget and evaluation. He has accompanied Education Secretary William J. Bennett to several appearances on Capitol Hill, and had emerged as one of the administration's spokesmen on its controversial student aid cuts.

Bauer's nomination had been delayed while Bennett's Hill critics gathered ammunition on an array of topics, hoping to turn the nomination vote into a referendum on Bennett's stewardship of the department.

But Bauer carefully avoided controversy at yesterday's hearing, conceding that he had little educational experience before joining the department and promising that he would uphold the law. On abolishing the department, he said he initially opposed it "as a conservative," but added, "Those of us who work there have an overwhelming responsibility to make sure it works in the best possible way." WASTE, FRAUD AND ABUSE . . . The Education Department's inspector general has uncovered $45.7 million in "questionable" payments to colleges and banks involved with department grants, programs and contracts, and has asked that at least $34 million be returned to the federal coffers.

In one of his semiannual reports to Congress, Inspector General James B. Thomas Jr. said the questionable expenses stem from fraud, abuse and mismanagement by some of the hundreds of institutions that receive Education Department money. The report covers the period from October 1984 through March of this year.

In separate criminal investigations stemming from the audits, 92 people were indicted and 61 were convicted. One case involved a woman who used 13 false names for more than a year to obtain $29,000 in U.S. government-backed student loan money. Another case involved a business office worker for an Ohio vocational school who forged student signatures on financial aid checks in a scheme to embezzle $15,000 in federal and state money.

The woman with the false names pled guilty and was given a two-year suspended sentence. The business office employe received a five-year suspended sentence.

Some of the other reported cases disclose complex, often bizarre schemes to bilk the department -- usually through the student loan program. One Indiana beauty school continued to award federal financial aid to students even after the school lost its eligibility to participate in the student aid program. Another student in New York was sentenced to three months in jail for applying for student loans using several Social Security numbers, including the number of his dead parent.

Some of the questionable costs resulted from sloppy recordkeeping by colleges and government officials. One state, for example, received $7.7 million more than it was entitled to for migrant education because state officials had overestimated the migrant population. SECULAR HUMANISM . . . The department has published its final regulations for school systems that want to apply for $75 million in funds designed to help desegregate school systems by creating "magnet" schools to attract students from other neighborhoods. The regulations define what is a minority and what is a properly eligible desegregation effort. But they fail to define "secular humanism."

The regulations prohibit local school districts from using magnet school money to teach "secular humanism," but it leaves it up to the school districts to figure out exactly what that means. The prohibition was included in the law that created the program in order to win the approval of Senate Labor and Human Resources Committee chairman Orrin G. Hatch (R-Utah). "Secular humanism" is a pejorative term that has been used by fundamentalists and New Right groups to describe a range of beliefs, from atheism to Darwinism to godless communism.