Dans lces cauchemars, deux hommes sont entrés chez moi pendant que je dormais.

les -> ces :
"les" is globally used to refer to a (more or less specific) generality
( Exemples
"Les chiens sont bruyants" : dogs are noisy (global)
"les chiens du voisins" : my neighbour's dogs (specific), but we are talking about all of them (general) )
"ces" those ones.

Formally "les cauchemars" is equivalent a generic "nightmares" (all of them). In the context it is pretty clear you refer to the two nightmares you just evoked. In french we would still make it explicit : "dans les deux cauchemars que j'ai fait".

The alternative is to use "ces", which is actually a direct reference to what you formerly introduced.
And we would even say "dans ces deux cauchemars" in order to make it clear that what comes after applies to both nightmares.


"pendant je <verbe>" --> "pendant que je <verbe>"... Well, that is the french way. Sorry.


"sont entrés" : I don't think the use of "passé composé" is formally a mistake, but somehow it makes me uneasy here. I'd personally go with "imparfait".
"Dans ces deux cauchemars, deux hommes entraient chez moi pendant que je dormais."
I think the use of "passé composé" makes it feel more descriptive of a real world event. On the other hand "imparfait" is more related to telling stories. So both are good. Just mind the fact that "passé composé" makes it more vivid and striking here.

J’avaits peur !

J’e leur ai crié dessus « Tu dois partir pas du tout ! » et heureusement les hommes sont partis sans problèmes.

The expression "crier dessus" actually exists, but it simply means "shout at", but it only stipulates who gets the noise, not the content of it.
"Mon chat m'a encore réveillé ce matin, et je te raconte pas comme je lui ai crié dessus." (My cat again woke me up this morning and, boy, I shouted it's head off"). A more familiar alternative would be "engueuler".

If you wanna shout something : " J'ai crié « cassez vous ! » "
If you wanna shout something at somebody : " J'ai crié à mon voisin indélicat « casses-toi ! » ."


« Tu dois partir pas du tout ! »
Sorry, but I don't get what you mean here...

Je me suis réveillée au milieu de la nuit à cause des cauchemars.

Not formally a mistake, so I won't correct in your text.
"des" --> "de ces" : a little bit like in the first sentence. Not formally a mistake in that context, we understand what nightmares you are talking about and it could even be considered part of your style. But we would be more specific.
"à cause des cauchemars" ~ "because of nightmares"
"à cause de ces cauchemars" ~ "because of these nightmares"

More natural :
"Je me suis réveillée deux fois dans la nuit à cause de ces cauchemars."

Je vais peut-être faire une sieste cet après-midi.

Perfect.

Just for you to know, "après-midi" is indeed masculine (because based on "midi", which is masculine). I actually had to check because many times in oral speech you people use a feminine version...

J’ai crié dessus « Tu dois partir pas du tout ! » et heureusement les hommes sont partis sans problèmes.

Pas du tout = not at all

Donc si tu écris « tu dois pas du tout partir » c’est un peu contradictoire :) it’s like saying « you don’t have to go at all! »