Not weird - just wrong, I'm afraid. Both 'refuse' and 'afford' have to be followed by 'to'+ infinitive.

Both afford and refuse must be used with the inifinitve. So you can even have a sentence with "I can't afford to".

'I can't afford entering the museum' and 'I refuse answering any more questions' are very acceptable English. '... entering the museum' and '...answering any more questions' would serve as noun phrases similar to: 'I can't afford this car' and 'I refuse your request'.

"I can't afford going out tonight." - perfect "I can't afford entering this museum! It's to expensive." - perfect, except it should be "too expensive" "I refuse answering any more questions" - perfect "I refuse to answer any more questions" - perfect Come to think of it, I don't think I've ever used the word "affording" in my whole life. If you're talking about being able to afford something, in the present tense, you should use "can afford" as you already did in your examples. "I'm affording this computer" sounds odd, "I can afford this computer" sounds natural. "Refusing" would be fine, depending on the sentence. "I am refusing to answer the question" would be good. I know it's not part of the question, but I would disagree with using "I've" in "Oh, and I just remembered I've the same questions with refuse." Although it's true that "I've" is short for "I have" I wouldn't use it in this sense. "I have gone to the store" could be "I've gone to the store" ("have" in the sense of "haber" in Spanish) "I have fruit" wouldn't be "I've fruit" ("have" in the sense of "tener" in Spanish)