1. "Instead of" is a preposition, and the only form of a verb that can function as the object of a preposition is the gerund (the -ing form.) You could also say, "Rather than ask questions" since "rather than" can function as a conjunction or as a preposition. 2. "Ask questions" isn't redundant in English. Think of it as the equivalent of "hacer preguntas" not "preguntar preguntas."

This is a good question. Neither of your choices is wrong, but both have poor style. To write the sentence in good style, you need to compare identical verb forms. For example, 1) "asking" can be compared with "thanking" 2) "to ask" can be compared with "to thank". 3) "ask" can be compared to "thank". Thus all of these sound good: "Instead of asking questions, I'd rather be thanking the Lord for giving this" or "Instead of to ask questions, I'd prefer to thank the Lord for giving this". or "Rather than ask questions, I'd thank the Lord for giving this". Present participles ("asking") and infinitives ("to ask") can both behave as nouns. That is why it is acceptable to use either as the object of "instead of". Any noun can be placed after "instead of". For example, "Instead of chocolate, I prefer vanilla", "instead of to ask, I prefer to thank".