What do you think?
1. Do you think that the old TSR D&D games are largely compatible?
2. What is your experience, if any, converting TSR material to 5e? 3e material? 4e material?
Aside from 1e/2e being, mostly, identical (with a minimum of conversion work needed), I'd say the various editions aren't so much compatible mechanically as they are conceptually. You can take an older module from previous editions and convert it to whichever edition you happen to be running it in, but I'd bet most would require some significant tweaking, the ease of which would depend greatly on the person's system mastery between the two (or more) systems. So, certainly doable, but requires a fair bit of knowledge. Of course, going from 1e -> 2e (or vice versa) requires little to no significant changes (though there are some gotchas of course). I can't speak to converting anything to or from 4e though, as I skipped it entirely (just wasn't my cup of tea).
I messed about with (somewhat) converting 2e's nonweapon proficiencies into 5e (as I find 5e's skill system and lack of any real progression there) a huge weakness of 5e. We (my group) tried it using just the 5e skills as they were, but it was ultimately limited by the small (compared to 1e/2e/3e/PF) number of available skills.
The basic approach was that each 5e class would receive a starting number of profs equal to the number they currently get (so the "choose X of the following skills). We then used the class groupings of 2e (Warrior, Priest, Rogue, Wizard) as a guide to determine nonweapon (skill) prof progression for each class. So you had Warrior (Barbarian, Fighter, Paladin, Ranger), Priest (Cleric, Druid, Monk), Rogue (Rogue, Bard), Wizard (Sorcerer, Warlock, Wizard). We ignored the grouping of what nonweapon profs could be taken by what class. The 2e progression didn't work so well (as Thieves/Bards were not the skill monkeys they have been since 3e), so we just used a universal progression of 1 new skill prof every 3 levels, so each class would earn 6 skills/profs over their career (3rd, 6th, 9th, 12th, 15th, 18th). With 18 skills and lots of tool profs to choose from, it worked well enough.
As we played we realized we really over-thought it initially. We didn't need to convert so much as just add a new skill/tool prof every 3 levels (of the player's choice to foster nifty character ideas). We eventually changed it to one new skill/tool prof every 4 levels (based on character level, not class level) to slow it down slightly and to foster a team effort approach to using skills/tools (some skills are still more useful for all to have than others). Even with backgrounds and subclasses and MC'ing adding possible new skill/tool profs, we've found this to work pretty darn well.