OrianaBanana Welcome! What team are you? 
Only level 23, is that why I’ve not encountered a lot of the Pokemon you are talking about?
No. Your level doesn’t determine what Pokémon you encounter; lower levels just mean the Pokémon you do encounter are likely to be much lower CPs and IVs.
If you’ve only been playing on and off then you will have missed several events, where they make certain Pokémon types more common to help you fill your Dex.
Your biome (the area in which you live) plays a major part. I personally get a lot of water Pokemon due to living near a lot of rivers, but other plays who live away from water won’t. And of course, now we have weather that affects spawns too.
Also, as new Gens arrive, older Gen Pokemon become rarer as their spawns have decreased. So Gen I Pokemon don’t appear anywhere near as frequently as they used to (hence the recent Kanto event), similarly with Gen II but not as much. When Gen IV is released, Gen III spawns will decrease.
This is why I’m really glad I’ve managed to complete Gen I, Gen II and Gen III Pokedexes (bar regionals not yet released in the UK and so far unreleased Pokémon) well in advance of them releasing Gen IV, as the longer it takes you to complete your Dex, the harder it will be.
DS (nearly 7) is crying because a Wailmer I was going to let him catch disappeared. Is this normal?
Yes. Pokemon only spawn for a certain amount of time, usually half an hour to forty five minutes, so if their time runs out before you manage to click on them, they will disappear.