Trying to get cute with component designators will be more trouble than it's worth. Ultimately it comes down to the basic problem that component usage is multi-dimensional and no linear naming scheme is going describe that well.
Sometimes I've seen people use 3 digit designators with the first digit identifying the schematic sheet. That's only one parameter, and doesn't help at all for finding the component on the board. It's also a hassle to maintain as you move components between sheets.
Even worse, very rarely I've seen people try to use numbering to identify which subcircuit something belongs to. For example, R1xx might be for the power supply, R2xx with the microcontroller, etc. This is even harder to maintain than the page scheme and less useful. OK, so R105 is probably part of the power supply. Now what? That gives me a rough idea of one of the many dimensions but does nothing for the others. Then there will be a large number of in-between cases where are part could be thought of as belonging to two or more subcircuits. This becomes a mess quickly and takes more effort and attention to maintain than it ever saves. Forgettaboutit, keep it simple.
As for trying to number them by value, that makes even less sense. That's what the BOM is for anyway. Having sequential numbers for each BOM line doesn't solve any problem I have ever encountered.
Let your software pick whatever numbers it wants to initially. As you edit the schematic, there may be gaps and things move around. Don't worry about it. When the schematic is all done or you're going to export it for others to look at, you can run a renumber utility if your software has that. That usually starts the numbering for each component type at 1 and goes up sequentially. They will probably be in some rough order by placement on the schematic, but don't count on that. Once you realize that component designator numbers are arbitrary labels, life becomes simpler.
No scheme is going to give you much information about part usage just from the number, so you need to make a cross reference listing anyway. I use Eagle and have created the INDEX ULP for that purpose. It makes a alphabetic list of all component designators and gives their schematic and board coordinates.
Yes.
It's not really clear what you are asking, but the answer is "yes" because Altium can do anything regarding PCB sizes.
Either...
...you mean that you have an existing design and want to "dice" it. In that case, just use cut/paste, as you would in any other software, to move whole sections of layout into a new PCB document.
Or...
...you mean that you have 4 smaller designs in your head and you want to draft them. In that case, create a separate PCB project for each.
Update: Re: Question Edits
From a pure manufacturing basis two 1 unit x 1 unit designs should never be cheaper than one 1 unit x 2 unit design ceteris paribus and assuming they all fit in one panel (which is almost always the case). If you are encountering cost anomalies with your vendor, contact your vendor and negotiate or switch vendors.
That said, there is no built-in functionality to auto-partition a design in the manner you have suggested because there is an insufficient business case for Altium (or any EDA company) to develop such functionality.
Cut-Paste will work fine, but as others have suggested, it's probably best to leave it as one larger PCB.
Best Answer
Around 0.15 min line width and 1.5 mm height should be big enough.
There isn't any standard about how to arrange the ref des in the PCB. Just try to make it as useful as you can. That's the reason that there is no point in putting it underneath of components.
As some mentioned, ellipsis (Rx.. Ry) are fine, as well rearranging the ref des in the same way than the physical components in a space nearby.
The key point is thinking about who is going to read/use that silkscreen.
If something is ambiguous, I would delete it. It can cause more problems.