Welcome!
I’m about to info dump on you a bit, so fair warning.
Also try to remember that these aren’t necessarily strict timings and lower levels are going to be very all over the place with things, often doing things that don’t make any sense (even in diamond I still see things that don’t make sense!)
With that said, standard 3rd base timings are somewhat dependent on a game-by-game basis as each game has different tells.
Hatch gas pool is often going to have an earlier 3rd base (around 2:30ish) but even this is subject to change - for example, depending on if a player is still mining gas after they’ve started ling speed or not. If they’ve continued mining gas, they might have a slightly delayed third base, or even chose not to get one at all as they might be going into faster roaches, for example.
A 3rd Command Center timing can be quite varied as well; obviously being matchup-dependent to an extent, but a standard 3rd base timing might be anywhere between 3:30 at the earliest, or very slightly earlier if you’re doing a 3CC opening, all the way to 4:00-5:00 which is much more common off a reaper expand into 1/1/1, or delayed even further (5:30-6:00 at the latest usually) if they’re getting their 2nd and 3rd Rax before their 3rd base, or they might have an extremely delayed one if they can’t kill you off an extremely dedicated 2 base timing (generally off 5 rax) - these are often all in though.
Mech again is completely different, but I don’t play a whole lot of mech to have an answer for your base timings there.
I can’t speak a whole lot for nexus timings outside of TvP. 3rd timings for a Nexus in TvP will almost always be earlier than the terran’s third base, around 3:30 (which is pretty greedy) to 4:30, unless they’re doing some sort of dedicated timing attack such as a blink timing.
As for scouting, again, that’s often matchup dependent.
Against Zerg, you’re looking for when they take their 3rd base, if they’re still mining gas after they get speed, when they put down their 2nd, 3rd and 4th gasses, if they take their 5th and 6th gas early etc. Gas timings can often indicate what tech they’re going for. Hydras will absolutely require 4 gasses where mutas will often require 6 because they’re extremely gas heavy, for example.
Protoss… Well there’s a reason why they say there’s a “Great Big Book of Protoss Bullsh!t”. They have a myriad of timings and attacks that they can hit you with, and any number of potential proxies; and a lot of them look extremely similar, but require very different counters depending on the matchup you’re playing. 1 gas styles with large gateway counts are often going to be chargelot timings, for example, while 3 gas might be blink. 2 gas will often be adept, while 4 could be DTs. - and that’s just off a twilight opener! Stargate openers are often very gas heavy so you’ll almost always see them at minimum need 2 gasses, but that could be oracle or void ray, and either can be an indicator of the style they intend to play (aggressive or defensive). Robo openers generally are early immortals or warp prisms, but could just as easily be for fast colossus or disruptors.
For Terran, you’re generally looking to differentiate between whether they’re meching or playing bio oriented playstyles. Very early 3rd gas is often an indicator of BC rushes; most bio pushes won’t require any more than 2 gasses at most, with the 2nd gas going down at the same time as the factory. Usually your 3rd and 4th gas will come down around the same time as your Ebays to have enough to double upgrade.
But the main tells you’re going to be looking for are the production structures and the timing for those. 3rd rax before the 3rd CC is going to have some sort of timing with a third base behind it, while 5 raxes is almost always going to be a 2 base all in - or at least an extremely dedicated timing.
Fast 2nd factory usually means mech, but could also potentially mean a blueflame hellbat build against Zerg, for example. The other thing you’re often looking for is a fast armoury - that’s a dead giveaway for a hellbat build, though those might be paired with banshees too. If they have a fast armoury and 1 tech-lab factory, it’s almost always going to be Thor drops, but that’s extremely uncommon.