For starters:
An argument is valid if and only if when all the premises are true, then the conclusion is true.
An argument is sound if and only if it is valid and all its premises are true
As for the logical form of your example arguments, you could formulate them as syllogisms - where a conclusion is made from two premises, each sharing a term in the conclusion and a term not in the conclusion.
Argument #1a)
Premise #1) Person X uses a proxy for their web activities.
Premise #2) All people who use a proxy for their web activities are hiding something.
Conclusion) Person X is hiding something.
This is a valid and sound argument, but, only trivially in the sense that proxy servers hide the users ip addy. Note tho that language use (and definition of terms) can be ambiguous. For example, in a trivial sense it does follow that using proxies necessarily entails that you are actually hiding something because the use of a proxy hides your i.p. addy. The implication that you are being deceitful, however, does not necessarily follow from the use of a proxy. Using "hiding something" to conclude deceit as a result of this reasoning would be a deductive fallacy:
Argument #1b)
Premise #1) Person X uses a proxy for their web activities.
Premise #2) All people who use a proxy for their web activities are hiding something.
Conclusion) Person X is deceitfully hiding something.
And this would be unsound:
Argument #1c)
Premise #1) Person X uses a proxy for their web activities.
Premise #2) All people who use a proxy for their web activities are deceitfully hiding something.
Conclusion) Person X is deceitfully hiding something.
Argument #2)
Premise #1) Person X dyed their hair red.
Premise #2) Some people that dye their hair red have trait Y.
Conclusion) Person X has trait Y.
The argument is not valid as only some and not all people with dyed red hair have trait Y - i.e. it does not follow that "dyeing hair red" entails "trait Y".
Note the distinctive uses of "some" and "all" in these two examples.
Lastly, I think we can also squeeze your third example argument into a syllogistic form to demonstrate its truth or fallacy:
Argument #3a)
Premise #1) Person X bought a gun.
Premise #2) Some people who buy guns plan crazy violence.
Conclusion) Person X is planning crazy violence.
Like the second example, it does not follow that Person X necessarily intends crazy violence. If however, premise #2 were true in this reformulation:
Argument #3b)
Premise #1) Person X bought a gun.
Premise #2) All people who buy guns plan crazy violence.
Conclusion) Person X is planning crazy violence.
...then the argument would be valid and sound.
As for interpreting the combination of Person X's lack of military background, lack of interest in joining the military and interest in researching military tactics... well, I'd recommend studying logistics instead of tactics ;)
Hope that helps. If you enjoy this kinda stuff, you might dig Harry J. Gensler's website: http://www.harryhiker.com/lc/