de or à between verbs, please?

Question

Below are examples of French sentences from a kwizik quiz:
In the first sentence, is there a rule to follow please, so I know to put de & not à between the conjugated verb refuser & verb lever? Speaking English, you would not say "refuse OF to lift", so I'd want to put an à, (if anything).
No. 1: Les voleurs refusent de lever les mains. (The thieves refuse to raise their hands.)
The 2nd sentence below, why put anything between matinée & écrire please? Doesn't écrire mean writing as well as 'to write'? The "à" already has a presence..!? The same point for sentence No. 3 below. The à is already contained within the infinitve form of the verb "espionner": TO spy.
No. 2: J'ai passé la matinée à écrire. (I spent the morning writing.)
No. 3: Elle s'amuse à espionner sa soeur. (She has fun spying on her sister.) 
Hoping someone will please shed some light..or rule.. about how to know which word to use: de or à, & why we need to put anything here at all ?
Cheryl

Accepted Answer

Bonjour Cheryl,
I'm afraid there is no simple rule. This is one of the trickiest aspects of French: some verbs require à (s'amuser à), some de (refuser de), some another preposition (s'habiller en, appuyer sur) and some no preposition at all (écouter, regarder, chercher). This is just something you have to memorize for each verb (similar to memorizing gender with each noun).
We don't yet have any specific exercises on Kwiziq, but you can see lists of verb sorted by preposition on our Partner site: French verbs with prepositions

Answer

Thanks Laura!
That's going to take a while to memorize them...I guess it'll happen bit by bit?
..while I'm here, I'll take this opportunity to ask if in the place where a photo could be put next to a person's name in Q&A, could I please have a "female" shadow, instead of a man's, in the place next to my name? I prefer not to put my photo up there.
Cheryl