Firstly, let's look at these idioms:
(The idiom) 'snoop around' action is intentionally done in order to find something secret or something about someone's personal life. The Free Dictionary describes it.
On the other hand, mind your own business is used when you don't want someone to ask or interfere about or in your personal life/affair. EnglishClub describes this with examples.
Stick one's nose in other people's affair means to interject one's self into another person's affairs. Implies that the interjection is unwanted -- OnlineSlangDictionary. As a side note, I have come more across poke someone's nose into.... as an alternative to this idiom.
Now your question:
The difference is snoop around is often carried out secretly generally to spy on someone or know the truth. If you snoop on a person, probably you are a detective and trying to find out the truths in that someone's life. A snooper is someone who makes uninvited inquiries into the private affairs of others. On the other hand, if you stick your nose in my life, you are trying to interfere in my life/personal affair. You are unnecessarily involving yourself in my matter. This could be someone's nature but the former one is not.
I'll try with examples:
I'm having doubts. I'll pay you for this. Just snoop around on my wife and find out who she's meeting every day.
Sure, you're good friends my wife. But let her make decisions on her own. Why do you stick your nose into her professional life? She's more capable enough to make a decision without your help.
There is a series of expressions in English starting with "just for" that mean "for no particular reason." Examples include:
Just for the sake of doing it
Just for the hell of it
Just for shits and giggles
Just for laughs
Just for fun
Just for kicks
One of these expressions is:
Just for a kick in the pants
In this context, "a kick in the pants" means "fun".
Normally, "a kick in the teeth" as an idiom means something like "a sudden and devastating event" or "a painful setback". However, in this context, it takes on the meaning of the primary expression, and the primary meaning is still "for no particular reason."
The secondary implication is that the behavior is known to be unproductive or disappointing--that he's not checking for any particular reason, but he keeps doing it, even though he know he's going to be disappointed every time he checks.
So the sentence might be rephrased something like:
I monitor this frequency every other day or so. I don't have any good reason to, and I know I'm never going to hear anything, but I do it anyway.
Best Answer
To "bite the bullet" means to accept that something unpleasant or difficult is sure to happen. It is often used when someone has tried easier or simpler alternatives for a task, but those methods have not been successful; however, trying other alternatives before going to the harder way is not required.
An easy way to remember this definition is to imagine a soldier biting a bullet while having emergency surgery on the battlefield with no medicine for pain. (This is often considered the origin of the phrase, but there is little evidence to support that claim.)
On the other hand, to "grit one's teeth" means to prepare for a challenge or strengthen one's will. This is a more general term, which can be used for a person dealing with any challenge, not necessarily an unavoidable one.
Anyone who is "biting the bullet" will probably "grit their teeth," but just because someone is "gritting their teeth" it doesn't necessarily mean they've "bitten a bullet."
EDIT to add requested examples:
Bob's car broke down on a highway in the middle of the desert. He tried to fix it himself but didn't know how. He tried flagging down someone passing by for a ride or to borrow a phone but nobody stopped. After a couple hours, Bob decided to bite the bullet and walk the 25 miles back to the last service station he passed.
Alice really wanted to make her school's football team. She was already tired from a day at the gym but she gritted her teeth and told herself to do one more set of push-ups so she could beat the competition.