Before 3.x this simply amounts to choosing a class.
I suspect this is largely true, though IIRC there were magic items (including some that specifically enhanced saves against death); magic item acquisition is certainly a part of character building in D&D. There may also have been NWPs but I don't know that one way or the other. But yes, limited options before 3e.
However, in 3e, there are plenty of options. Every level you take affects saves. Ability scores and anything that changes them. Feats. Resistance bonuses. Maximizing your saves is a significant part of building a 3e character.
Again, prior to 3.x the rule for surprise was "the party is surprised on a 1 or 2". How do you avoid that?
They had divinations before 3e, didn't they? They had talking to people and finding out what the threats are in the area in advance?
But again, limitations of pre-3e rules are significant, but 3e gives us the important perception and stealth skills and a number of spells and special abilities that help you see what's coming.
Yep, good old "old school" play - "memorise the MM or you're toast".
Again, 3e has knowledge skills to explicitly deal with this, while 2e had some NWPs that were more limited, as I recall.
How do you avoid surprise, anticipate encounters or counter dangerous/SoD abilities when no edition has had actual explicit rules for doing any of this?
Well, I've covered surprise and anticipation enough, so there's rules for that, but yes there are also explicit rules for countering. What do you think Death Ward is? That predates 3e. There's also other spells and items that give you save bonuses or more qualified immunities. If it's a gaze attack (Medusa) there's also the whole averting your eyes business. With an enemy spellcaster, there's counterspelling and disruption. If we're including "save or suck" abilities, many of those are subject to dispel and break enchantment.
There's also broader tactics. If it's a death effect with limited range, you can just stay out of range. Many SoD monsters are not particularly mobile and don't have other combat options, so sniping is quite viable against, say, a bodak. In other cases, the death effect may be targeted, in which case, sending in your backstab-y rogue or pulling out invisibility spells may be quite effective.
Easy - you play "blag the DM". More formally, you invite the DM to use their power to improvise additional rules on the spot to allow the regular rule (if any) to be bypassed or to allow priviledges of information or exemption from power effects that are not a part of the normal rules.
I see nothing inherently wrong with improvisational play, but that's completely irrelevant to the situation at hand, as there are ample explicit rules that deal with the subject.
If you have few hit points you need to be extremely careful, if you have lots you can be a bit more adventurous; there's the most basic application of skill right there.
Perhaps you missed the whole debate in some other thread recently (blanking on which one) about whether characters know how many hp they have and whether that counts as metagaming. But yes, that is a (very basic) application of skill.
The point is that there are things that are written into the game that you can do to mitigate the risk. Absent significant DM license, with SoD there seldom is.
Except, you know, all that stuff about specific spells, averting one's eyes, and so on.
Another comment was made about "starting out of range of the SoD effect"; with line of sight effects or in a "dungeon" that's usually not a real option.
Don't be silly. There's a cantrip specifically for opening and closing doors at a distance. There's summoning garbage monsters to go ahead for you. There's perception skills and clairvoyance and other such divinations to help you see what's waiting for you. Dungeons do present an unusual set of circumstances, but you still shouldn't be just barging into a room with no idea what's going on, and people who play in dungeons ought to know how to deal with threats in confined spaces. And if, for any reason, a powerful opponent gets within 30 ft. of you without you knowing anything about it, you're in deep trouble whether it has an SoD or not.