Partially true. Those types of inspections are limited to "Customs Officers" which means CBP, ICE and some other specifically trained law enforcement.
Depends on the conditions and situation. While CBP are usually the law enforcement personnel at the crossing point (ICE is usually involved with interior operations), there are also Agriculture and DEA and others in play at times.
State and local police are also sometimes involved if such laws are pertinent. I have been at the Blaine, WA crossing when wanted/armed and dangerous people came through who were arrested and turned over to Washington authorities.
There are also incidents at preclearance facilities for air travel located outside the USA (in Canada, Bermuda, Aruba) where local police can be involved, e.g., the RCMP (Mounties) in Canada, where US authorities have no jurisdiction.