Nothing is going to improve your ability with anything as much as simply getting more and better spells

This is just kind of generally true. You will always be best at whatever it is you want to do by maximizing the number and level of spells you know. More sorcerer levels (or levels in prestige classes that advance sorcerer spellcasting) will always improve you more than levels in anything else.

The PHB, in particular, is really harsh on sorcerers who want to dabble elsewhere

There are extremely limited options. The prestige classes were all written for wizards first: whereas a wizard qualifies for loremaster without even trying, you would have to burn a ton of your very-limited spells known, plus you don’t get enough knowledge skills in-class, so cross-class ranks and entering the class much later are your only options. Archmage is better, but only comes very late, and still puts a sharp requirement on your spells known, while a wizard can trivially fill up his spellbook with whatever he needs to get in.

Furthermore, sorcerers start off a level behind wizards (well, starting at 3rd level), so taking a class that doesn’t advance spellcasting is very painful. As already stated, none of them provide sufficient benefit to justify the move from a purely-optimal standpoint.

The optimal path for your character is just single-classed sorcerer, even though it doesn’t get any class features. The spells are just that good. Between mage armor, grease, glitterdust, fly, solid fog, dimension door, contingency, polymorph, teleport, planar binding, moment of prescience, foresight, gate, shapechange, and time stop, your options for protecting yourself are some of the best in the game. You can boost your defenses, nullify threats, and keep out of harm’s way better than almost anyone.

But optimizing isn’t necessarily the goal here

You have ~2 levels to play with, you want to tone down your advantages over the rest of your party, and you’d like to be a bit more survivable. Well, how does an average of 6 HP and +4 to all saves over single-classed sorcerer sound? With the promise of that save bonus increasing as you improve. Paladin 2 gets Divine Grace, which adds your (very large) Charisma to all saving throws. It also has a d10 HD, and gets that juicy +3 Fortitude just for having it as a good save.

This is a common “sorcadin” build, and paladin 2/sorcerer 18, while definitely and distinctly worse than sorcerer 20, does have some nice things going for it, particularly in the saves category. The weapon and armor proficiencies are nice enough (though without access to supplements, mage armor is still your best armor), plus if you really wanted you could go for eldritch knight (not really recommended, another lost level would suck and you don’t get much for it). In theory, arcane archer 2 for Imbue Arrow is also an option, but that’s 5 lost spellcasting levels relative to a wizard, so you only barely get 8th-level spells; Imbue Arrow’s not worth that.

There is, however, a problem:

• The PHB paladin is Lawful Good-only

Now, when I play, we ignore this rule. Because ultimately, what works for the game is going to depend massively on the character and story. Alignment is too generic and broad to accurately suggest precisely what is or is not appropriate for a character or a story; it’s all-but-impossible to truly have a good one-size-fits-all system. Therefore, I strongly recommend considering these kinds of “fluff restrictions” critically, and to make sure that they are actually improving your game. I often find that they would instead have a negative impact, and thus often ignore them. One of my most successful, long-running, and favorite characters was a devout worshiper of a staunchly anti-undead religion – whose primary class was dread necromancer. Why your CN sorcerer would gain divine grace depends on a lot of variables in your game, but ultimately, in my experience, not only can this sort of thing be explained convincingly, determining convincing explanations fleshes out the character and improves the game and story.

Furthermore, there are, in the wider world of 3.5 supplements, numerous options for supplanting both of these problems; there are paladin variants that allow other alignments, and so on. You don’t have access to them, but the fact that they exist should be a good case to make to your DM.

While we’re on the subject of paladin variants you don’t have access to, there is one that trades detect evil at-will for inspire courage +1, 1/day, at 1st level. That’s an excellent trade. Alternatively, a ranged smite variant exists; that just is exactly like smite evil except it applies to ranged attacks instead of melee attacks. In your case, of course, it’d probably be smite law though.

Yes. Each level selected provides cumulative benefits.

This also applies to skill points and base attack bonus. See the section on multi-classing in the PHB or the SRD (under classes) for details. As you are selecting base classes, there are usually no prerequisites (see monk and paladin for exceptions).

Please note that when leveling up and selecting prestige classes, those may have prerequisites which are required to be met before taking that level. There are other small details, but it does not seem relevant to your question, so I will avoid expounding.