Okay, these are actually both legal questions, so I’m going to take them both. Up front, I’m not a lawyer; I took a few pre-law classes in college before realizing that my liver wouldn’t survive law school. So, if you’re in a situation where these aren’t abstract questions for writing, go find an actual lawyer immediately. Now, with that out of the way:
On weapons? Short answer: no. If it’s a weapon, there’s going to be places you can’t take it legally. This goes across the board from firearms to staves, to knives. Sooner or later, you’re going to go one of those places.
On top of that, weapon laws vary pretty wildly based on a lot of specific details. A knife that’s legal in one state won’t always be legal in another. For instance: spring loaded knives (Switchblades and OTP tacticals) are legal in South Dakota and Wyoming, but illegal in Washington and California. Some states measure blade length, but stop measuring it when the blade becomes serrated, while others don’t care about serration, and will simply classify a knife as a weapon based on its overall length. A pocket knife (with something under a 2 inch blade) is perfectly legal in most places, but you can’t take it into a TSA cordon. Even, Firearms, which are legal with the proper licensing in most places, are illegal in DC.
There are improvised weapons you can usually get through a security checkpoint, or even a frisking reliably. A heavy key ring or a nice heavy ballpoint pen, for instance. But, police and security guards who are working a checkpoint have one job; keep people from taking things through. Tactical pens may sound like a good idea, but it’s a huge red flag to a cop at a checkpoint. They read the same things you do, and they know when a pen is designed to be a concealable weapon.
As to how much force you can use to defend yourself? Yeah, this is also a very complex subject. Basically under most American law, if threatened, you can defend yourself, but you can only use enough force to allow yourself to retreat to safety.
What constitutes a threat varies from state to state, and can vary from case to case, based on context. Sometimes, technical assault is necessary before you can defend yourself, other times, the threat of violence is sufficient.
How much force you can use depends on who you are, how well trained you are, and what the situation is. If your character is a black belt, they’re going to be on a much tighter leash than someone who had one self defense seminar in college.
Justifiable homicide requires that you are in immediate, reasonable, fear for your life, and cannot retreat to any safety. Someone must be trying to kill you, and you cannot have another option. But, we’re back to the context part, some states have laws called “Stand your Ground laws”, or “Castle Laws”, these allow you to use lethal force when you have an option to retreat. Some states, require that you be in your home for them to take effect, (California and New York, as I recall), while others only require that someone is attacking you, (Texas and, now rather infamously, Florida).
Also, justifiable homicide is, what’s known as an “affirmative defense”, that means, you’ll get arrested, go to trial, and then, instead of saying, “no, I didn’t do this,” you effectively say, “yes, I did this, but I had to because of X.”
I’m going to step back a bit, and say this; if you’re going to use the law and legal consequences in your writing, you’re going to need to do a lot of reading, and a lot of research. Watching a lot of the original Law & Order series is helpful, but it’s not going to cut it. Most states have their criminal code posted online, these days, and from what I remember, most libraries should have a legal section.
When you’re reading it, just take it slow, and be very literal about everything. When you hit a reference to somewhere else in the code, look it up, find out what that means, and come back. It can take some time and effort, but it will give you useful information.
Additionally, you should find a friend or friend of the family who is a lawyer and pick their brains for as much as you can. Law, like medicine and a few other fields, is one of those areas where it’s basically impossible for a writer to fake it, and still get a good story.