If it involves the government it involves the constitution, the government has no other source of authority. How can the government process anybody (foreign or not) without the constitution if the only authority base is the constitution. Your mixing some things below this (1) military authority which the courts have ruled exists under the constitution and (2) what is the minimum requirement under the constitution for processing a non US citizen inside the US. Your current post mostly speaks of #1. however your question is really #2 Our current Presidential staff is out of control and will eventually be reeled in by the courts. The process is idiotic because it will weaken the future Presidents and US Military leaders. The court is trying to allow the military powers to stay in place however Bush continues to abuse the actual power pushing for a fight he can not win. The courts have ruled the military can both peace and war time procedures for soldiers and captives. These are not unlimited powers, they are powers deemed necessary to efficiently defend the US. So taking a suspected person is allowed, indefinite detention with out charge is not allowed. Thus the foolishness of today, the court allowed extended time to process the detainees but the president appears to be waiting out the court by refusing to process these people. It is a matter of time until the court intervenes. That intervention may affect Mexicans mowing yards in Phoenix. Or it may not. As mentioned earlier the current standard is reasonable proof the person is not a legal US citizen. At that time they can be jailed or deported not beaten, murdered, tortured, executed, etc, etc.
so to review your specific
1st amendment - Do you expect a religion requirement, or should they be jailed based on their personal opinions?
4th amendment - if you start illegal searching what do you do when no illegal is found? Do you think it okay for the government to breakdown your door ripe your house apart stop your car when ever they feel like it , then say well we were looking for non US citizens?
5th amendment - about the same as number 4 if you are ripped from your bed at night and deported as an illegal alien is that okay as long as the paper work says you were believed to be illegally in the US? No court, no lawyer, no trial is that acceptable to you? See only if you have a fair trail could you explain you are US citizen but if you want to prevent this constitutional amendment from being activated during immigration round ups well then you have to suffer.
6th amendment - more of the same, do you need a trial or not? are you willing to be deported because the police did not have to follow these amendments because they thought you were illegal.
#10 - you already spoke against this idea of rogue police actions being allowed.
#14 - your citizenship was granted by birth as was mine, so if you want to change that what should be the new method to determine if the next baby will or will not be granted citizenship?