You write like someone that already posts here!  :)

Most of the people you see standing around talking are full time.  It is hard to fire them.  Main reasons to get fired are stealing and attendance.  There is nothing in the union handbook that dictates a certain performance.

The best way to move up in Kroger is to always perform at your best.  Eventually, someone will take notice and make sure you get moved up.

This makes it hard on a DH when they have slackers working for them.  I constantly have to ride my crew like a red headed step child to get work done.  They say I am mean.  I say no work will get done if I don't say anything.  Most of these people will not last. If they do, they will always be making minimum wage and not go far in Kroger.

Store managers and co managers give write-ups.  The DH can suggest the write-up.  I have never seen anyone written up for talking.  I suppose a person could be written up for not helping a customer with the 3 As.

Not a DH or Management.

Its Kroger, don't work so hard. Its not worth it. Do your job, break a sweat, but don't kill yourself with work.

"What can and can't you be written up for?"
The shortest answer, and most applicable for the average clerk is "Anything if they think you won't file a grievance." Most writeups I have seen or heard of have been illegitimate on some count, and the clerks in question simply had no idea that they could grieve it.
On a more technical level, insubordination, swearing, some failures of job duties, attendance, having a coffee with you while on the clock, violation of posted notices threatening disciplinary action, to name a few. Remember though, for something to be legitimate insubordination, they must have phrased the item in question as an order. If they said "If you have time, do X" and write you up for it if it isn't done, thats no good.

There is also the potential issue of precedent. If several clerks at your store habitually arrive five to ten minutes late for their shift without discipline, but you are written up for being one to five minutes late, the writeup may possibly be thrown out via grievance.

You must remember, they are often instructed to disregard the contract in store operations as much as they can get away with. Literally, you may be written up for anything at management discretion and its up to you to know if and when to fight it.

"Who is able to write you up?"
Management only. If it comes from management, its legitimate. If any hourly clerk gives you some kind of disciplinary writeup, its trash as members of the bargaining unit are not to discipline each other directly. That should be in any contract, but as always check your own local contract for accuracy.

There are extra hoops possible as well. For instance, you offend manager X in private. Manager X initiates a writeup against you. This can potentially be thrown out, as the offended party in cases of insubordination or disrespect should not also be the same to issue discipline. Further, there should be some attempt to investigate if the allegation is true by whatever other manager would be assigned then to deal with that.

"How many write-ups before you get fired?"
Variable based on location, the nature of the infraction, and store management.
A lot of Kroger's rules say "up to and including discharge" so a lot of discipline can potentially lead to being fired immediately. With that in mind, its then entirely up to how much the store management wants to keep the clerk. They may immediately fire people they dislike, use a write up or two to act as a warning to a mediocre employee, and a highly valuable troublemaker might get four in a month without being fired, or have their problems ignored as per management's disciplinary discretion.

"Do they have to come to YOU and give YOU warnings before they can write you up?"
That is entirely up to your local contract, and there is some pretty wide variability within the different locals. Most likely yes.

"Is managers allowed to inform other employees about your write ups and/or your work performance?"
Unless you can make a harassment style case, they can do whatever they want in that regard. As always, they are essentially allowed to do nearly anything until a grievance is filed. Failure to grieve is viewed by management tacit compliance with a practice.

"I get called in all the time. . ."
Guessing you are working on front end. The front end is a messed up place at every store for schedules and reliable workers. I know your pain, but the thing to realize is that especially on the front end, for Kroger's math just not quitting is a bonus from an employee. The simple act of showing up most or even half of the time makes most of these people valuable enough to not go through the hiring process to replace them. Retail work is almost universally undesirable, and because of that any shred of work getting done by people is far more valuable to the business than the clerk level vantage point would suggest. Add to that most of the potential advancement at Kroger takes longer than other competing businesses or is far less valuable than other businesses and its easy to see why they aren't as concerned about what bad employees they have, even more so when some hard workers pick up the slack.

I'm a pretty "pro-union" dude, but don't let the above fool you. All of that is theory. In practice, many of those protections fail and its entirely up to you to know the strength of your local union. Depending on area, management may well have the final say in a grievance, and unless there are legal implications for the company, some areas will automatically deny all grievances unless they wish to show mercy or else to punish the lower level store management. In practice, discipline is completely open to your store unless whatever they are doing is CLEARLY and DEMONSTRABLY illegal.  Resistance to this is a crap shoot based on the relative power and mood of your union local and management. About the only things you can get reliable protection on are scheduling and seniority issues.