To clear up most of page 6, the bill of rights and the remainder of the constitution don't bestow rights on anyone. Rather, it acknowledges the principles that human beings DO have those rights without the need to spell it out, and thereby limits the government's ability to intrude upon them. You can do whatever the hell you want until a law deems it illegal. But no law can be made that infringes on what is established in the constitution as an inalienable right.
Regarding illegal aliens and the constitutional protections, in state law there is no check to confirm someone is a citizen. If a cop searches an illegal alien without probable cause, then there is a remedy to be had, as the constitution prevents unlawful action by the state, irrespective of the person searched.
The takeaway is that the constitution is a limit on the government's power. You don't have a legal right to free speech. Instead, you have a right to be free from unreasonable limitations of speech by the government under most situations.