The infinitive form of a verb is has the functions of being the name of the verb, but also expressing the verb abstractly as a hypothetical idea or concept. "To run a marathon would require a lot of training." [I've never done it] The gerund form of the verb has the function of expressing activity. "Running marathons involves a lot of training." [It's something I or other people do a lot] Consider this construction : it is + adjective + infinitive e.g. It is necessary to run a lot before taking part in a marathon. Other common examples of adjectives in this construction are "possible", "useful", "hard", "easy", "sensible". I don't know for sure why we should not use the -ing form here, but my best guess is because we are considering the verb hypothetically, or in the abstract.

basically it is because it is subjunctive . The way you put "be-" before verbs to show doubt or uncertainty, so it must be in infinitive form , not continuous. گاهي سخت باشد You would use the subjunctive bashe instead of ast.

because hamlet is saying aya vojud dashte basham ya vojud dashte nabasham not aya vojud daram ya vojud nadarm

For your 2nd problem English does not always have so many rules, you must memorize what structures are correct. Word order and punctuation are very important. For example you can correctly use "using" with a comma and it will have a more wistful feeling: "Sometimes it is hard, not using a dictionary." or it is also correct if you change the structure because the entire phrase "not using a dictionary" takes the place of "it": "Sometimes not using a dictionary is hard." In: "Sometimes it is hard not to use a dictionary. " you are emphasizing the word "not" when you say it and implying that you are comparing it to the act of using a dictionary.