ولما كانت حضرته العلية مطمح الآمال، ومسرح هِمَم الرجال، ومحطَّ رحال الفضائل، ومثابة أمن الخائف ومُنْية السائل، توخى الزمان خدمتها ببدائع تُحَفه وروائع طُرَفه
I can’t access dictionaries anymore until later this evening, but here’s what I know:
مطمح never heard of it, but as you pointed out it’s clearly a مفعل "place form", and طموح means ambition (at least in MSA), so مطمح الآمال sounds slightly redundant to me but maybe a dictionary will clear this up.
مسرح همم الرجال = the theater of concerns (or interests, that’s an ambiguous word even in MSA) of men
محط رحال الفضائل = the station/place of convergence (this too is a pretty vague word, but also used in MSA) of worthy/virtuous (plural of فاضل I suppose) travellers (I’m assuming this is the plural of راحل)
مثابة أمن = no idea, the first word usually means "quality" (of being someone, as in status, or rank) or "equivalence", so I’m not sure.
مُنية I don’t know this word but the root looks like أمنية and تمنى which are related to hoping, wishing, etc. So maybe something like : (and when the Caliph ) was seen as a place of safety for the one who fears (الخائف) and of hope for the one who asks (or has a request = السائل)
توخى in MSA usually means "to be prepared for" or "anticipate" etc. with an idea of due diligence and prudence. So literally I would guess "fate (الزمان) decided to be at his service thrrough his unique wonders (بديع means innovative, but it also refers to anything astonishing/stunning, and تحفة is a wonder, or something wonderful (hence museum = متحف i.e. the place where you store wonders).
روائع probably is the plural of روعة which usually means "awesomeness" but then why "awsomenesses" I don’t know... and طرف is again a plural, logically it would be the plural of طُرْفَة but I’ve never seen such a word, however the adjective طريف is common and refers to something nice and out of the ordinary.
Sorry I can’t be more specific at the moment.