Learn English – Matched vs. Matching

They don't mean the same thing. They're not the same part of speech.

Select as an adjective has a different meaning from selected.

First of all, I've got to say that I agree with the comments you've gotten so far, in that select countries does not work well with volcanoes. In fact, I actually find it to be crude.

Second,select does mean special, but countries aren't really special for having a natural disaster occur on their soil. It's not something fortunate.

Often, in the US, you'll hear opening soon in select cities, in reference to film releases. In that context, it means specially selected cities. It also can indicate a limited, small-market film release. And it's fine to use it that way. But I would not recommend saying something like the bombings occurred in select cities. Select has a positive connotation.

As for selected, it's the past tense of the verb form of select, meaning to pick or to choose. So if you say, branches opening soon in selected cities, you mean to say that these locations were hand-picked. It doesn't have to be hand-picked; items can be selected by machines too.

If selected items are on sale, then they were picked, chosen, or designated by management. You're referring to the selection (noun) process.

If select items are on sale, then there's something special, unique, or valuable about those items. Here, select is modifying the noun items. It's not referring to the process of selection, but they may be items you'd very much like to select (verb meaning choose).

By placing 'branches' in select cities the brand did nothing to the cities and there's no city with very unique quality in this matter. It'll be 'selected cities'.

This can actually be either one. With opening branches in select cities, it means they were selected because there is something unique about them. Maybe they're unsaturated markets, or maybe they were chosen because the business thought they'd be more profitable in those cities. If they're opening in selected cities, that just means that the branch locations have already been selected.

Had it been the Olympic Committee's matter, we would have said, "They organize the event in select countries."

Actually, they organize the events in the selected city. At the same time, the IOC chooses from select cities.

I also think that you should put the unit of measure after the word one, but I'll leave it out in this analysis.

All items have weight one. 
All items have weights one.  
All items have the weight one. 

If you are trying to say here that each individual item in a set weighs one, you would say "Each item has a weight of one" or "all the items have a weight of one." The latter is a bit ambiguous, though, since it could mean that all the items taken together have a weight of one as well.

The weight of all items is one. 

This would mean that the total weight of all items in existence is one. "The weight of all the items is one" means that all the items taken together weigh one. "The weight of each item is one" means that every item in the set weighs one.

The weights of all items are one. 

As above, this means all items in existence. However, now you are (probably) saying that every individual item in existence weighs one. More correct would be to say "The weight of every item is one" if you wished to convey this idea.

All items weights are one. 
All items' weight is one. 

These are both grammatically wrong. The grammatically correct sentence is "All items' weights are one." The meaning is the same as "The weights of all items are one" and my comment there applies here.

Now, I would say "Each item weighs one" to mean that every individual item weighs one, and "All the items together weigh one" to mean that the total weight of all the items is one.