Can you give more context? Maybe a sentence before those sentences? The first one is incorrect, as it is. You can't beam in on anyone. The second one is also incorrect, you wouldn't say "I'd pulled" it's incorrect grammar. If you give more context I can help you with the meaning.

It depends on the sentence..There isn't really a way to know how and when to use them. Although, gerund's sound more natural, using an infinitive can *sometimes* make you sound... "hoity".. They mean the same thing. Here are some examples: Gerund- Reading is my favorite hobby Infinitive- To read is my favorite hobby The gerund sounds 100% more natural Gerund- I like eating Infinitive- I like to eat Both of these sound completely natural! Some times it's only acceptable to use one or the other. Example: I want to eat -infinitive. I want to eating- gerund. This is 100% incorrect. do not say this. If you're using "want" then you'll use an infinitive! This also goes for "need" as another example. Check out these two links, they list verbs that require a gerund and verbs that require infinitives :) http://www.englishpage.com/gerunds/gerund_list.htm http://www.englishpage.com/gerunds/infinitive_list.htm

It depends on the sentence.. Sometimes it sounds better to use "so that" and other times it sounds okay using "so."

I'm not sure of the first one, but Шапка can be hat or cap, it doesn't matter :) But in the US, we usually call them "beanies." I guess it's a slang term.

You would just say "female doctor" and "male doctor," or go gender neutral and say "doctor."