Phrase Usage – Is ‘I’ll Call You at My Convenience’ Rude Compared to ‘I’ll Call You When I Am Available’?

I would say it like this, probably:

There is a lot of noise (or commotion) at your end. Can you please speak louder?

At least in the U.S., "at your end" seems more natural than "on your side." We often say things like, "on your end of the phone" (or "on my end of the phone").

In the context of cell phone usage, I might regard a disturbance as poor reception. You've asked about a noisy room, which is why I prefer commotion.

When talking about a particular food or meal, eat and have can function interchangeably most of the time. Of the two, have is the more versatile and generic word:

Let's start with your last example:

I'm eating pizza now. Let me call you back – I don't want my pizza getting cold.
I'm having pizza now. Let me call you back – I don't want my pizza getting cold.

I see no real difference in those two statements. I think I'd be more likely to use the first, but the second wouldn't jar my native ear.

Then your breakfast example:

I eat breakfast every day at 8 o'clock.
I have breakfast every day at 8 o'clock.

Once again, either one of those is okay, although the second sounds a little bit more formal for some reason. In its seventh definition for have, Macmillan mentions:

have (verb) [TRANSITIVE] [NEVER PASSIVE] to eat or drink something. This word is often used in polite offers and requests

• Can I have another piece of that delicious cake?
• Let me buy you a drink. What’ll you have?
• Why don’t you stay and have lunch with us?

I’ll have (=used for requesting food or drink in a restaurant): I’ll have the roast beef, please.

There are a few places where the two words aren't interchangeable. The end of that definition gives one example; if I was ordering at a restaurant, I wouldn't say, "I'll eat the roast beef, please." That might be true, if that's what I'm ordering – but it's simply not idiomatic to say it that way.

Another clue is that have is always transitive. So, it's perfectly fine to say:

I'm starving – let's eat!

but you wouldn't be able to say:

I'm starving – let's have!

Here's one more odd case:

I'm hungry; let's have at that hamburger place.
I'm hungry; let's eat at that hamburger place.

In this case, we can't use have to mean eat, because we're not using the word transitively. We can fix that by saying:

I'm hungry; let's have hamburgers at that place.

However, the first is not necessarily grammatically incorrect, because we could be using the phrasal verb have at. NOTE: This would be a very informal usage of have at, but I give it a mention because it shows how complex and flexible English can be, especially when dealing with informal expressions and eating food. When I was in college, one of my roommates might have said:

I'm hungry; I think I hear hamburgers calling my name!