Yes, they do. You absolutely give up freedom of speech and any rights of unreasonable search and seizure when you enlist. You don't give up every right, though. You still get the option of a jury trial whenever you want one. A commander's ability to levy administrative punishment relies on you opting in. You always have the option to seek court martial instead, the issue being they can levy much more severe punishments.
Military members still have freedom of speech rights. More tightly regulated in some instances than civilians, but the right isn't taken away. Even as a civilian there are restrictions on your freedom of speech.
Similar for the fourth amendment. There are exceptions for civilians, and a different set of exceptions for military members, based on government need.
The Constitution applies to all US citizens, military or not.
