Docent P wrote:habite une banlieue
The "à" is absent. Is this correct, not a misprint?
No no, you don't need to put "à" here... Hmm... in fact, you say "à" when it's definite. When talking about a precise town, for example, "il habite à Rouen", but as "une banlieue" means "a suburb" (that is to say in any suburb), it's not definite, so you can not say "à une banlieue".
Docent P wrote:>de la tête de la famille
"le chef de la famille" ?
"Le neveu du chef de famille" would be right here.
Docent P wrote:>C'est il qui inviter une
"C'est lui qui invente une..."
Grammatically it's correct, but you can't invent an idea, you find it, so "C'est lui qui trouve une idée géniale" would be better.
Docent P wrote:>repose la bûche en retour
"en retour" doesn't work well for "back"?
I should better have said "reprende la bûche", right?
What do you want to say? He puts it back? If so, it's "il la repose" (simply) "reprendre"means "to take back".
Docent P wrote:>catafalque arrive
"char funèrbe" works well?
"catafalque" is the same word than in English (I have checked in the dictionnary to see what it means... I didn't know this word

)
"char funèbre" = "hearse" in english.
(choose according to what you want to say)
Docent P wrote:>...se met à crier
He has begun doing sth - il se met à qch - does it work well for any verb or just for "crier"?
The -ing form in english is very often translated in french by "se mettre à faire qqchose", as we don't have any real equivalent. It works for any verb, it just depends on the context.