‘お父さん（おとうさん）’ is the polite way to say ‘father,’ and should be used whenever you are referring to someone else’s father. It can also be used in the second person to address someone like the patriarch of your homestay family. Though this would sound horrifically awkward in English, it is very common to use the polite version of family words (such as ‘おばあさん’ and ‘お姉さん（おねえさん）’) to refer directly to people you are not actually related to.
‘今日（きょう）’ is a kanji compound with an irregular reading. Neither the character ‘今’ nor the character ‘日’ have this reading associated with them outside of this word. These irregular compounds are the exception and not the rule in Japanese writing, but they are not uncommon throughout the language—their readings must be memorized, as there are no rules in place to govern their unique pronunciations.
The question is asking us what Mary’s host father did today. We hear him reply that he watched television at home. Note that he uses the end-of-sentence particle ‘よ’ to emphasize that he is answering a direct question. This translates roughly to ‘I tell you what’ or something similar, though it does not have a regional character as it would in English. We arrive at this answer:
お父さんは今日うちでテレビを見ました。
おとうさんはきょううちでテレビをみました。

The question is asking us what Mary’s host father did today. We hear him reply that he watched television at home. Note that he uses the end-of-sentence particle ‘よ’ to emphasize that he is answering a direct question. This translates roughly to ‘I tell you what’ or something similar, though it does not have a regional character as it would in English. We arrive at this answer:
お父さんは今日うちでテレビを見ました。
おとうさんはきょううちでテレビをみました。

‘お母さん（おかあさん）’ is the polite way to say ‘mother,’ and should be used whenever you are referring to someone else’s mother. It can also be used in the second person to address someone like the matriarch of your homestay family. Though this would sound horrifically awkward in English, it is very common to use the polite version of family words (such as ‘おばあさん’ and ‘お姉さん（おねえさん）’) to refer directly to people you are not actually related to.
The question is asking us what Mary’s host mother did. When Mary’s host father tells her that he was watching TV earlier that day, Mary asks if he did so alone. By way of explanation, her host father tells her that his wife (whom he refers to as ‘mother,’ which is not uncommon for a parent/host-parent to do when talking to their child/host-child) went to the store. We arrive at this answer:
お母さんは友達とデパートに行きました。
おかあさんはともだちとデパートにいきました。

The question is asking us what Mary’s host mother did. When Mary’s host father tells her that he was watching TV earlier that day, Mary asks if he did so alone. By way of explanation, her host father tells her that his wife (whom he refers to as ‘mother,’ which is not uncommon for a parent/host-parent to do when talking to their child/host-child) went to the store. We arrive at this answer:
お母さんは友達とデパートに行きました。
おかあさんはともだちとデパートにいきました。

‘お父さん（おとうさん）’ is the polite way to say ‘father,’ and should be used whenever you are referring to someone else’s father. It can also be used in the second person to address someone like the patriarch of your homestay family. Though this would sound horrifically awkward in English, it is very common to use the polite version of family words (such as ‘おばあさん’ and ‘お姉さん（おねえさん）’) to refer directly to people you are not actually related to.
‘明日（あした）’ is a kanji compound with an irregular reading. Neither the character ‘明’ nor the character ‘日’ regularly have this reading associated with them outside of this word. These irregular compounds are the exception and not the rule in Japanese writing, but they are not uncommon throughout the language—their readings must be memorized, as there are no rules in place to govern their unique pronunciations.
The question is asking us what Mary and her host-father are going to do tomorrow. After her host-father tells her that his wife is out shopping with her friend, Mary asks what else he is doing today. He gives a non-response, and Mary invites him to play tennis tomorrow, which they agree to do. We arrive at this answer:
メアリーさんとお父さんは明日テニスをします。
メアリーさんとおとうさんはあしたてにすをします。

The question is asking us what Mary and her host-father are going to do tomorrow. After her host-father tells her that his wife is out shopping with her friend, Mary asks what else he is doing today. He gives a non-response, and Mary invites him to play tennis tomorrow, which they agree to do. We arrive at this answer:
メアリーさんとお父さんは明日テニスをします。
メアリーさんとおとうさんはあしたてにすをします。