It is very slow going.
I find the games that run the smoothest are the ones where the DM makes all rolls. The difference between:
DM: There's an orc in the fog.
Player: I attack!
DM: Roll to hit.
Player: Natural 19 - that's a threat!
DM: Yup - roll to confirm.
Player: AC 13.
DM: Hit, but not a critical. But don't forget, 20% miss chance...
Player: 41%, no problem.
DM: Roll damage.
Player: 11!
DM: The orc collapses in a heap.
vs
DM: There's an orc in the fog.
Player: I attack!
DM: A solid hit - 11 damage. The orc collapses in a heap.
(Admittedly, that's an exaggerated - but not unheard of - example.)
It gets worse as soon as players start requesting clarifications about details and so on, or if the state of the battlefield changes mid-round (the orc everyone said they wanted to attack dies on the first character's action, so everybody else's declared actions become irrelevant, and allthe players have to post again...)
Again, games run smoother if players trust the DM to make sensible decisions on their behalf in that sort of case. It also helps if the players post conditions on their actions. (If the orc is still alive, I'll attack him, otherwise I'll grab the pie!)
But the ultimate truth of PbEMs is: Combats
crawl. That doesn't mean you should avoid them... you just need to be aware that they slow the game right down.
Pure roleplay elements, in contrast, can go quite quickly... but it does depend on how often people respond. I've seen fifty messages exchanged between three people who all happen to be online within an hour... and then other players check their mail in the morning and panic
"How many posts per day" really comes down to the guidelines the DM sets down, and the availability of the players. You have to be fairly flexible in allowing someone in a different time zone to slot their remarks into a conversation that took place while the player was in bed!
But yeah, a short conversation can take a few days. A long combat can take a month. Going up a level might take over a year, or less than a month, depending on the game.
You get used to it. Things simply don't happen as fast as they do in a table game.
-Hyp.