Most (if not all) of the problems listed in the question are related to the Pokemon GO servers being offline, slow to respond, or overloaded with requests.
In the meantime, nobody likes not playing the game. Fortunately, there are a few things you can do:
- Just Wait
The easiest (and best) move to take is just to wait for the servers to restore to a normal state. You can check the server status at this handy page, or by just trying to log in to the game.
- Force Quit the App
Sometimes, the app will get stuck in a cycle of failure and will be unable to actually do anything. You can fix this by [iOS] opening the Multitasking window and swiping up on Pokemon GO, or [Android] navigating to Settings > Apps > Pokemon GO and then touching the Force Quit button.
- [Android] Clear Caches/Data
As a more extreme measure, you can go to Settings > Apps > Pokemon GO and tap the Clear Data button. Note that this will only delete your local data -- your Pokemon will be safe. However, you will need to log in again. Be sure you know what account you used/created for Pokemon GO if you do this.
- Reinstall the App
If all else fails, you can just go the nuclear option and erase the entire app and start again. If you have an existing account (and you know the credentials used), your Pokemon will be at no risk and will all be there once you log in again.
If you want to level up fast:
TL;DR:
Save evolutions for lucky egg effects.
Lucky eggs double all of the experience you gain for the 30 minutes after you use them. You get a lucky egg once you reach level 9 and every multiple of 5 thereafter (10, 15, 20, etc.). You can also buy them from the store for Pokécoins (which can be purchased with real money). Being under their effect at all times that you're playing the game will make you level up extremely fast right off the bat, but if you don't want to spend the money and want to level up efficiently the old fashioned way:
- catch every Pokémon you can find, send extra ones to the professor*
- visit Pokéstops
- ignore gyms (for now)
- don't spend candy
- don't spend stardust
- don't evolve (for now)
* Keep enough Pokémon to evolve them:
If you have collected ~50 Pidgey candy you can evolve 4 Pidgeys (12
candy each), so you have to keep 4 Pidgeys in your inventory. (For
other Pokémon check how many candy they need to evolve and keep enough
of them)
If you have accumulated enough Pokémon to evolve and their candy you can use a lucky egg and evolve them all at once. It's recommended to use cheap Pokémon for this, like Pidgey, Caterpie, etc., which cost 12 candy to evolve[1]. Also it is useful to use lure modules and incense with your lucky egg and double the catch XP as well while evolving your zoo.
When you reached a decent level and you start caring about gyms you can then start spending stardust. Don't waste it as it gets more and more expensive to power up Pokémon later. It's not necessarily needed to level up, but keeps the fun factor higher. If you want to power up a few Pokémon make sure to power up Pokémon with higher CP as they need much less stardust to get combat ready.
Edit for clarification
[1] Of course you can keep more expensive ones as well (like Rattata) and evolve them with the egg effect enabled. If you're really running out of space by that time make sure to keep the ones, where you don't have the evolved form in your Pokédex, yet, in order to also get the "first catch" bonus x2.
Best Answer
There isn't one, unless it fits one of the typical min-max desired attributes:
Other than that, there's no point in keeping them as they are also fodder Pokemon, or if you intend to at some point mass-purify them.
Just a note: Fodder shadow is more valuable than regular fodder Pokemon as they have lower costs when upgraded using candy (like Lucky Pokemon) once you purify them, so if moves and IVs aren't your goal: That's a reason to keep them (ie. a shadow Bulbasaur with bad IVs versus a regular Bulbasaur with also bad IVs)